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9 | 2239-2242 | 6
10
) Z
1 2
10
J
C
C
d
−
×
×
=
×
= 3 84 × 10–16 Z m
The atomic number of foil material gold is Z = 79, so that
d (Au) = 3 0 × 10–14 m = 30 fm |
9 | 2240-2243 | 2
10
J
C
C
d
−
×
×
=
×
= 3 84 × 10–16 Z m
The atomic number of foil material gold is Z = 79, so that
d (Au) = 3 0 × 10–14 m = 30 fm (1 fm (i |
9 | 2241-2244 | 84 × 10–16 Z m
The atomic number of foil material gold is Z = 79, so that
d (Au) = 3 0 × 10–14 m = 30 fm (1 fm (i e |
9 | 2242-2245 | 0 × 10–14 m = 30 fm (1 fm (i e fermi) = 10–15 m |
9 | 2243-2246 | (1 fm (i e fermi) = 10–15 m )
The radius of gold nucleus is, therefore, less than 3 |
9 | 2244-2247 | e fermi) = 10–15 m )
The radius of gold nucleus is, therefore, less than 3 0 × 10–14 m |
9 | 2245-2248 | fermi) = 10–15 m )
The radius of gold nucleus is, therefore, less than 3 0 × 10–14 m This
is not in very good agreement with the observed result as the actual
radius of gold nucleus is 6 fm |
9 | 2246-2249 | )
The radius of gold nucleus is, therefore, less than 3 0 × 10–14 m This
is not in very good agreement with the observed result as the actual
radius of gold nucleus is 6 fm The cause of discrepancy is that the
distance of closest approach is considerably larger than the sum of
the radii of the gold nucleus and the a-particle |
9 | 2247-2250 | 0 × 10–14 m This
is not in very good agreement with the observed result as the actual
radius of gold nucleus is 6 fm The cause of discrepancy is that the
distance of closest approach is considerably larger than the sum of
the radii of the gold nucleus and the a-particle Thus, the a-particle
reverses its motion without ever actually touching the gold nucleus |
9 | 2248-2251 | This
is not in very good agreement with the observed result as the actual
radius of gold nucleus is 6 fm The cause of discrepancy is that the
distance of closest approach is considerably larger than the sum of
the radii of the gold nucleus and the a-particle Thus, the a-particle
reverses its motion without ever actually touching the gold nucleus 12 |
9 | 2249-2252 | The cause of discrepancy is that the
distance of closest approach is considerably larger than the sum of
the radii of the gold nucleus and the a-particle Thus, the a-particle
reverses its motion without ever actually touching the gold nucleus 12 2 |
9 | 2250-2253 | Thus, the a-particle
reverses its motion without ever actually touching the gold nucleus 12 2 2 Electron orbits
The Rutherford nuclear model of the atom which involves classical
concepts, pictures the atom as an electrically neutral sphere consisting
of a very small, massive and positively charged nucleus at the centre
surrounded by the revolving electrons in their respective dynamically
stable orbits |
9 | 2251-2254 | 12 2 2 Electron orbits
The Rutherford nuclear model of the atom which involves classical
concepts, pictures the atom as an electrically neutral sphere consisting
of a very small, massive and positively charged nucleus at the centre
surrounded by the revolving electrons in their respective dynamically
stable orbits The electrostatic force of attraction, Fe between the revolving
electrons and the nucleus provides the requisite centripetal force (Fc) to
keep them in their orbits |
9 | 2252-2255 | 2 2 Electron orbits
The Rutherford nuclear model of the atom which involves classical
concepts, pictures the atom as an electrically neutral sphere consisting
of a very small, massive and positively charged nucleus at the centre
surrounded by the revolving electrons in their respective dynamically
stable orbits The electrostatic force of attraction, Fe between the revolving
electrons and the nucleus provides the requisite centripetal force (Fc) to
keep them in their orbits Thus, for a dynamically stable orbit in a
hydrogen atom
Fe = Fc
2
2
2
0
1
4 ε
=
π
e
mv
r
r
(12 |
9 | 2253-2256 | 2 Electron orbits
The Rutherford nuclear model of the atom which involves classical
concepts, pictures the atom as an electrically neutral sphere consisting
of a very small, massive and positively charged nucleus at the centre
surrounded by the revolving electrons in their respective dynamically
stable orbits The electrostatic force of attraction, Fe between the revolving
electrons and the nucleus provides the requisite centripetal force (Fc) to
keep them in their orbits Thus, for a dynamically stable orbit in a
hydrogen atom
Fe = Fc
2
2
2
0
1
4 ε
=
π
e
mv
r
r
(12 2)
Rationalised 2023-24
Physics
296
Thus the relation between the orbit radius and the electron
velocity is
2
2
0
4
e
r
εmv
=
π
(12 |
9 | 2254-2257 | The electrostatic force of attraction, Fe between the revolving
electrons and the nucleus provides the requisite centripetal force (Fc) to
keep them in their orbits Thus, for a dynamically stable orbit in a
hydrogen atom
Fe = Fc
2
2
2
0
1
4 ε
=
π
e
mv
r
r
(12 2)
Rationalised 2023-24
Physics
296
Thus the relation between the orbit radius and the electron
velocity is
2
2
0
4
e
r
εmv
=
π
(12 3)
The kinetic energy (K) and electrostatic potential energy (U) of the electron
in hydrogen atom are
2
2
2
0
0
1
and
2
8
4
e
e
K
mv
U
r
r
ε
ε
=
=
= −
π
π
(The negative sign in U signifies that the electrostatic force is in the –r
direction |
9 | 2255-2258 | Thus, for a dynamically stable orbit in a
hydrogen atom
Fe = Fc
2
2
2
0
1
4 ε
=
π
e
mv
r
r
(12 2)
Rationalised 2023-24
Physics
296
Thus the relation between the orbit radius and the electron
velocity is
2
2
0
4
e
r
εmv
=
π
(12 3)
The kinetic energy (K) and electrostatic potential energy (U) of the electron
in hydrogen atom are
2
2
2
0
0
1
and
2
8
4
e
e
K
mv
U
r
r
ε
ε
=
=
= −
π
π
(The negative sign in U signifies that the electrostatic force is in the –r
direction ) Thus the total energy E of the electron in a hydrogen atom is
2
2
0
0
8
4
e
e
E
K
U
r
r
ε
ε
=
+
=
−
π
π
2
0
8
e
εr
= −
π
(12 |
9 | 2256-2259 | 2)
Rationalised 2023-24
Physics
296
Thus the relation between the orbit radius and the electron
velocity is
2
2
0
4
e
r
εmv
=
π
(12 3)
The kinetic energy (K) and electrostatic potential energy (U) of the electron
in hydrogen atom are
2
2
2
0
0
1
and
2
8
4
e
e
K
mv
U
r
r
ε
ε
=
=
= −
π
π
(The negative sign in U signifies that the electrostatic force is in the –r
direction ) Thus the total energy E of the electron in a hydrogen atom is
2
2
0
0
8
4
e
e
E
K
U
r
r
ε
ε
=
+
=
−
π
π
2
0
8
e
εr
= −
π
(12 4)
The total energy of the electron is negative |
9 | 2257-2260 | 3)
The kinetic energy (K) and electrostatic potential energy (U) of the electron
in hydrogen atom are
2
2
2
0
0
1
and
2
8
4
e
e
K
mv
U
r
r
ε
ε
=
=
= −
π
π
(The negative sign in U signifies that the electrostatic force is in the –r
direction ) Thus the total energy E of the electron in a hydrogen atom is
2
2
0
0
8
4
e
e
E
K
U
r
r
ε
ε
=
+
=
−
π
π
2
0
8
e
εr
= −
π
(12 4)
The total energy of the electron is negative This implies the fact that
the electron is bound to the nucleus |
9 | 2258-2261 | ) Thus the total energy E of the electron in a hydrogen atom is
2
2
0
0
8
4
e
e
E
K
U
r
r
ε
ε
=
+
=
−
π
π
2
0
8
e
εr
= −
π
(12 4)
The total energy of the electron is negative This implies the fact that
the electron is bound to the nucleus If E were positive, an electron will
not follow a closed orbit around the nucleus |
9 | 2259-2262 | 4)
The total energy of the electron is negative This implies the fact that
the electron is bound to the nucleus If E were positive, an electron will
not follow a closed orbit around the nucleus 12 |
9 | 2260-2263 | This implies the fact that
the electron is bound to the nucleus If E were positive, an electron will
not follow a closed orbit around the nucleus 12 3 ATOMIC SPECTRA
As mentioned in Section 12 |
9 | 2261-2264 | If E were positive, an electron will
not follow a closed orbit around the nucleus 12 3 ATOMIC SPECTRA
As mentioned in Section 12 1, each element has a characteristic spectrum
of radiation, which it emits |
9 | 2262-2265 | 12 3 ATOMIC SPECTRA
As mentioned in Section 12 1, each element has a characteristic spectrum
of radiation, which it emits When an atomic gas or vapour is excited at
low pressure, usually by passing an electric current through it, the emitted
radiation has a spectrum which contains certain specific wavelengths
only |
9 | 2263-2266 | 3 ATOMIC SPECTRA
As mentioned in Section 12 1, each element has a characteristic spectrum
of radiation, which it emits When an atomic gas or vapour is excited at
low pressure, usually by passing an electric current through it, the emitted
radiation has a spectrum which contains certain specific wavelengths
only A spectrum of this kind is termed as emission line spectrum and it
EXAMPLE 12 |
9 | 2264-2267 | 1, each element has a characteristic spectrum
of radiation, which it emits When an atomic gas or vapour is excited at
low pressure, usually by passing an electric current through it, the emitted
radiation has a spectrum which contains certain specific wavelengths
only A spectrum of this kind is termed as emission line spectrum and it
EXAMPLE 12 3
Example 12 |
9 | 2265-2268 | When an atomic gas or vapour is excited at
low pressure, usually by passing an electric current through it, the emitted
radiation has a spectrum which contains certain specific wavelengths
only A spectrum of this kind is termed as emission line spectrum and it
EXAMPLE 12 3
Example 12 3 It is found experimentally that 13 |
9 | 2266-2269 | A spectrum of this kind is termed as emission line spectrum and it
EXAMPLE 12 3
Example 12 3 It is found experimentally that 13 6 eV energy is
required to separate a hydrogen atom into a proton and an electron |
9 | 2267-2270 | 3
Example 12 3 It is found experimentally that 13 6 eV energy is
required to separate a hydrogen atom into a proton and an electron Compute the orbital radius and the velocity of the electron in a
hydrogen atom |
9 | 2268-2271 | 3 It is found experimentally that 13 6 eV energy is
required to separate a hydrogen atom into a proton and an electron Compute the orbital radius and the velocity of the electron in a
hydrogen atom Solution Total energy of the electron in hydrogen atom is –13 |
9 | 2269-2272 | 6 eV energy is
required to separate a hydrogen atom into a proton and an electron Compute the orbital radius and the velocity of the electron in a
hydrogen atom Solution Total energy of the electron in hydrogen atom is –13 6 eV =
–13 |
9 | 2270-2273 | Compute the orbital radius and the velocity of the electron in a
hydrogen atom Solution Total energy of the electron in hydrogen atom is –13 6 eV =
–13 6 × 1 |
9 | 2271-2274 | Solution Total energy of the electron in hydrogen atom is –13 6 eV =
–13 6 × 1 6 × 10–19 J = –2 |
9 | 2272-2275 | 6 eV =
–13 6 × 1 6 × 10–19 J = –2 2 ×10–18 J |
9 | 2273-2276 | 6 × 1 6 × 10–19 J = –2 2 ×10–18 J Thus from Eq |
9 | 2274-2277 | 6 × 10–19 J = –2 2 ×10–18 J Thus from Eq (12 |
9 | 2275-2278 | 2 ×10–18 J Thus from Eq (12 4), we have
2
18
0
2 |
9 | 2276-2279 | Thus from Eq (12 4), we have
2
18
0
2 2
10
J
8 ε
−
= −
= −
×
eπ
E
r
This gives the orbital radius
2
9
2
2
19
2
18
0
(9
10 N m /C )(1 |
9 | 2277-2280 | (12 4), we have
2
18
0
2 2
10
J
8 ε
−
= −
= −
×
eπ
E
r
This gives the orbital radius
2
9
2
2
19
2
18
0
(9
10 N m /C )(1 6
10
C)
8
(2)(–2 |
9 | 2278-2281 | 4), we have
2
18
0
2 2
10
J
8 ε
−
= −
= −
×
eπ
E
r
This gives the orbital radius
2
9
2
2
19
2
18
0
(9
10 N m /C )(1 6
10
C)
8
(2)(–2 2
10
J)
e
r
E
ε
−
−
×
×
= −
= −
π
×
= 5 |
9 | 2279-2282 | 2
10
J
8 ε
−
= −
= −
×
eπ
E
r
This gives the orbital radius
2
9
2
2
19
2
18
0
(9
10 N m /C )(1 6
10
C)
8
(2)(–2 2
10
J)
e
r
E
ε
−
−
×
×
= −
= −
π
×
= 5 3 × 10–11 m |
9 | 2280-2283 | 6
10
C)
8
(2)(–2 2
10
J)
e
r
E
ε
−
−
×
×
= −
= −
π
×
= 5 3 × 10–11 m The velocity of the revolving electron can be computed from Eq |
9 | 2281-2284 | 2
10
J)
e
r
E
ε
−
−
×
×
= −
= −
π
×
= 5 3 × 10–11 m The velocity of the revolving electron can be computed from Eq (12 |
9 | 2282-2285 | 3 × 10–11 m The velocity of the revolving electron can be computed from Eq (12 3)
with m = 9 |
9 | 2283-2286 | The velocity of the revolving electron can be computed from Eq (12 3)
with m = 9 1 × 10–31 kg,
6
0
2 |
9 | 2284-2287 | (12 3)
with m = 9 1 × 10–31 kg,
6
0
2 2
10 m/s |
9 | 2285-2288 | 3)
with m = 9 1 × 10–31 kg,
6
0
2 2
10 m/s 4
e
v
εmr
=
=
×
π
Rationalised 2023-24
297
Atoms
consists of bright lines on a
dark
background |
9 | 2286-2289 | 1 × 10–31 kg,
6
0
2 2
10 m/s 4
e
v
εmr
=
=
×
π
Rationalised 2023-24
297
Atoms
consists of bright lines on a
dark
background The
spectrum emitted by atomic
hydrogen
is
shown
in
Fig |
9 | 2287-2290 | 2
10 m/s 4
e
v
εmr
=
=
×
π
Rationalised 2023-24
297
Atoms
consists of bright lines on a
dark
background The
spectrum emitted by atomic
hydrogen
is
shown
in
Fig 12 |
9 | 2288-2291 | 4
e
v
εmr
=
=
×
π
Rationalised 2023-24
297
Atoms
consists of bright lines on a
dark
background The
spectrum emitted by atomic
hydrogen
is
shown
in
Fig 12 5 |
9 | 2289-2292 | The
spectrum emitted by atomic
hydrogen
is
shown
in
Fig 12 5 Study of emission
line spectra of a material can
therefore serve as a type of
“fingerprint” for identification
of the gas |
9 | 2290-2293 | 12 5 Study of emission
line spectra of a material can
therefore serve as a type of
“fingerprint” for identification
of the gas When white light
passes through a gas and we
analyse the transmitted light
using a spectrometer we find
some dark lines in the
spectrum |
9 | 2291-2294 | 5 Study of emission
line spectra of a material can
therefore serve as a type of
“fingerprint” for identification
of the gas When white light
passes through a gas and we
analyse the transmitted light
using a spectrometer we find
some dark lines in the
spectrum These dark lines
correspond precisely to those wavelengths which were found in the
emission line spectrum of the gas |
9 | 2292-2295 | Study of emission
line spectra of a material can
therefore serve as a type of
“fingerprint” for identification
of the gas When white light
passes through a gas and we
analyse the transmitted light
using a spectrometer we find
some dark lines in the
spectrum These dark lines
correspond precisely to those wavelengths which were found in the
emission line spectrum of the gas This is called the absorption spectrum
of the material of the gas |
9 | 2293-2296 | When white light
passes through a gas and we
analyse the transmitted light
using a spectrometer we find
some dark lines in the
spectrum These dark lines
correspond precisely to those wavelengths which were found in the
emission line spectrum of the gas This is called the absorption spectrum
of the material of the gas 12 |
9 | 2294-2297 | These dark lines
correspond precisely to those wavelengths which were found in the
emission line spectrum of the gas This is called the absorption spectrum
of the material of the gas 12 4 BOHR MODEL OF THE HYDROGEN
ATOM
The model of the atom proposed by Rutherford assumes
that the atom, consisting of a central nucleus and
revolving electron is stable much like sun-planet system
which the model imitates |
9 | 2295-2298 | This is called the absorption spectrum
of the material of the gas 12 4 BOHR MODEL OF THE HYDROGEN
ATOM
The model of the atom proposed by Rutherford assumes
that the atom, consisting of a central nucleus and
revolving electron is stable much like sun-planet system
which the model imitates However, there are some
fundamental differences between the two situations |
9 | 2296-2299 | 12 4 BOHR MODEL OF THE HYDROGEN
ATOM
The model of the atom proposed by Rutherford assumes
that the atom, consisting of a central nucleus and
revolving electron is stable much like sun-planet system
which the model imitates However, there are some
fundamental differences between the two situations While the planetary system is held by gravitational
force, the nucleus-electron system being charged
objects, interact by Coulomb’s Law of force |
9 | 2297-2300 | 4 BOHR MODEL OF THE HYDROGEN
ATOM
The model of the atom proposed by Rutherford assumes
that the atom, consisting of a central nucleus and
revolving electron is stable much like sun-planet system
which the model imitates However, there are some
fundamental differences between the two situations While the planetary system is held by gravitational
force, the nucleus-electron system being charged
objects, interact by Coulomb’s Law of force We know
that an object which moves in a circle is being
constantly accelerated – the acceleration being
centripetal in nature |
9 | 2298-2301 | However, there are some
fundamental differences between the two situations While the planetary system is held by gravitational
force, the nucleus-electron system being charged
objects, interact by Coulomb’s Law of force We know
that an object which moves in a circle is being
constantly accelerated – the acceleration being
centripetal in nature According to classical
electromagnetic theory, an accelerating charged particle
emits radiation in the form of electromagnetic waves |
9 | 2299-2302 | While the planetary system is held by gravitational
force, the nucleus-electron system being charged
objects, interact by Coulomb’s Law of force We know
that an object which moves in a circle is being
constantly accelerated – the acceleration being
centripetal in nature According to classical
electromagnetic theory, an accelerating charged particle
emits radiation in the form of electromagnetic waves The energy of an accelerating electron should therefore,
continuously decrease |
9 | 2300-2303 | We know
that an object which moves in a circle is being
constantly accelerated – the acceleration being
centripetal in nature According to classical
electromagnetic theory, an accelerating charged particle
emits radiation in the form of electromagnetic waves The energy of an accelerating electron should therefore,
continuously decrease The electron would spiral
inward and eventually fall into the nucleus (Fig |
9 | 2301-2304 | According to classical
electromagnetic theory, an accelerating charged particle
emits radiation in the form of electromagnetic waves The energy of an accelerating electron should therefore,
continuously decrease The electron would spiral
inward and eventually fall into the nucleus (Fig 12 |
9 | 2302-2305 | The energy of an accelerating electron should therefore,
continuously decrease The electron would spiral
inward and eventually fall into the nucleus (Fig 12 6) |
9 | 2303-2306 | The electron would spiral
inward and eventually fall into the nucleus (Fig 12 6) Thus, such an atom can not be stable |
9 | 2304-2307 | 12 6) Thus, such an atom can not be stable Further,
according to the classical electromagnetic theory, the
frequency of the electromagnetic waves emitted by the
revolving electrons is equal to the frequency of
revolution |
9 | 2305-2308 | 6) Thus, such an atom can not be stable Further,
according to the classical electromagnetic theory, the
frequency of the electromagnetic waves emitted by the
revolving electrons is equal to the frequency of
revolution As the electrons spiral inwards, their angular
velocities and hence their frequencies would change
continuously, and so will the frequency of the light
emitted |
9 | 2306-2309 | Thus, such an atom can not be stable Further,
according to the classical electromagnetic theory, the
frequency of the electromagnetic waves emitted by the
revolving electrons is equal to the frequency of
revolution As the electrons spiral inwards, their angular
velocities and hence their frequencies would change
continuously, and so will the frequency of the light
emitted Thus, they would emit a continuous spectrum,
in contradiction to the line spectrum actually observed |
9 | 2307-2310 | Further,
according to the classical electromagnetic theory, the
frequency of the electromagnetic waves emitted by the
revolving electrons is equal to the frequency of
revolution As the electrons spiral inwards, their angular
velocities and hence their frequencies would change
continuously, and so will the frequency of the light
emitted Thus, they would emit a continuous spectrum,
in contradiction to the line spectrum actually observed Clearly Rutherford model tells only a part of the story
implying that the classical ideas are not sufficient to
explain the atomic structure |
9 | 2308-2311 | As the electrons spiral inwards, their angular
velocities and hence their frequencies would change
continuously, and so will the frequency of the light
emitted Thus, they would emit a continuous spectrum,
in contradiction to the line spectrum actually observed Clearly Rutherford model tells only a part of the story
implying that the classical ideas are not sufficient to
explain the atomic structure FIGURE 12 |
9 | 2309-2312 | Thus, they would emit a continuous spectrum,
in contradiction to the line spectrum actually observed Clearly Rutherford model tells only a part of the story
implying that the classical ideas are not sufficient to
explain the atomic structure FIGURE 12 5 Emission lines in the spectrum of hydrogen |
9 | 2310-2313 | Clearly Rutherford model tells only a part of the story
implying that the classical ideas are not sufficient to
explain the atomic structure FIGURE 12 5 Emission lines in the spectrum of hydrogen Niels Henrik David Bohr
(1885 – 1962) Danish
physicist who explained the
spectrum of hydrogen atom
based on quantum ideas |
9 | 2311-2314 | FIGURE 12 5 Emission lines in the spectrum of hydrogen Niels Henrik David Bohr
(1885 – 1962) Danish
physicist who explained the
spectrum of hydrogen atom
based on quantum ideas He gave a theory of nuclear
fission based on the liquid-
drop model of nucleus |
9 | 2312-2315 | 5 Emission lines in the spectrum of hydrogen Niels Henrik David Bohr
(1885 – 1962) Danish
physicist who explained the
spectrum of hydrogen atom
based on quantum ideas He gave a theory of nuclear
fission based on the liquid-
drop model of nucleus Bohr contributed to the
clarification of conceptual
problems
in
quantum
mechanics, in particular by
proposing the comple-
mentary principle |
9 | 2313-2316 | Niels Henrik David Bohr
(1885 – 1962) Danish
physicist who explained the
spectrum of hydrogen atom
based on quantum ideas He gave a theory of nuclear
fission based on the liquid-
drop model of nucleus Bohr contributed to the
clarification of conceptual
problems
in
quantum
mechanics, in particular by
proposing the comple-
mentary principle NIELS HENRIK DAVID BOHR (1885 – 1962)
Rationalised 2023-24
Physics
298
EXAMPLE 12 |
9 | 2314-2317 | He gave a theory of nuclear
fission based on the liquid-
drop model of nucleus Bohr contributed to the
clarification of conceptual
problems
in
quantum
mechanics, in particular by
proposing the comple-
mentary principle NIELS HENRIK DAVID BOHR (1885 – 1962)
Rationalised 2023-24
Physics
298
EXAMPLE 12 4
FIGURE 12 |
9 | 2315-2318 | Bohr contributed to the
clarification of conceptual
problems
in
quantum
mechanics, in particular by
proposing the comple-
mentary principle NIELS HENRIK DAVID BOHR (1885 – 1962)
Rationalised 2023-24
Physics
298
EXAMPLE 12 4
FIGURE 12 6 An accelerated atomic electron must spiral into the
nucleus as it loses energy |
9 | 2316-2319 | NIELS HENRIK DAVID BOHR (1885 – 1962)
Rationalised 2023-24
Physics
298
EXAMPLE 12 4
FIGURE 12 6 An accelerated atomic electron must spiral into the
nucleus as it loses energy Example 12 |
9 | 2317-2320 | 4
FIGURE 12 6 An accelerated atomic electron must spiral into the
nucleus as it loses energy Example 12 4 According to the classical electromagnetic theory,
calculate the initial frequency of the light emitted by the electron
revolving around a proton in hydrogen atom |
9 | 2318-2321 | 6 An accelerated atomic electron must spiral into the
nucleus as it loses energy Example 12 4 According to the classical electromagnetic theory,
calculate the initial frequency of the light emitted by the electron
revolving around a proton in hydrogen atom Solution From Example 12 |
9 | 2319-2322 | Example 12 4 According to the classical electromagnetic theory,
calculate the initial frequency of the light emitted by the electron
revolving around a proton in hydrogen atom Solution From Example 12 3 we know that velocity of electron moving
around a proton in hydrogen atom in an orbit of radius 5 |
9 | 2320-2323 | 4 According to the classical electromagnetic theory,
calculate the initial frequency of the light emitted by the electron
revolving around a proton in hydrogen atom Solution From Example 12 3 we know that velocity of electron moving
around a proton in hydrogen atom in an orbit of radius 5 3 × 10–11 m
is 2 |
9 | 2321-2324 | Solution From Example 12 3 we know that velocity of electron moving
around a proton in hydrogen atom in an orbit of radius 5 3 × 10–11 m
is 2 2 × 10–6 m/s |
9 | 2322-2325 | 3 we know that velocity of electron moving
around a proton in hydrogen atom in an orbit of radius 5 3 × 10–11 m
is 2 2 × 10–6 m/s Thus, the frequency of the electron moving around
the proton is
(
)
6
1
11
2 |
9 | 2323-2326 | 3 × 10–11 m
is 2 2 × 10–6 m/s Thus, the frequency of the electron moving around
the proton is
(
)
6
1
11
2 2
10 m s
2
2
5 |
9 | 2324-2327 | 2 × 10–6 m/s Thus, the frequency of the electron moving around
the proton is
(
)
6
1
11
2 2
10 m s
2
2
5 3
10
m
v
r
ν
−
−
×
=
=
π
π
×
» 6 |
9 | 2325-2328 | Thus, the frequency of the electron moving around
the proton is
(
)
6
1
11
2 2
10 m s
2
2
5 3
10
m
v
r
ν
−
−
×
=
=
π
π
×
» 6 6 × 1015 Hz |
9 | 2326-2329 | 2
10 m s
2
2
5 3
10
m
v
r
ν
−
−
×
=
=
π
π
×
» 6 6 × 1015 Hz According to the classical electromagnetic theory we know that the
frequency of the electromagnetic waves emitted by the revolving
electrons is equal to the frequency of its revolution around the nucleus |
9 | 2327-2330 | 3
10
m
v
r
ν
−
−
×
=
=
π
π
×
» 6 6 × 1015 Hz According to the classical electromagnetic theory we know that the
frequency of the electromagnetic waves emitted by the revolving
electrons is equal to the frequency of its revolution around the nucleus Thus the initial frequency of the light emitted is 6 |
9 | 2328-2331 | 6 × 1015 Hz According to the classical electromagnetic theory we know that the
frequency of the electromagnetic waves emitted by the revolving
electrons is equal to the frequency of its revolution around the nucleus Thus the initial frequency of the light emitted is 6 6 × 1015 Hz |
9 | 2329-2332 | According to the classical electromagnetic theory we know that the
frequency of the electromagnetic waves emitted by the revolving
electrons is equal to the frequency of its revolution around the nucleus Thus the initial frequency of the light emitted is 6 6 × 1015 Hz It was Niels Bohr (1885 – 1962) who made certain modifications in
this model by adding the ideas of the newly developing quantum
hypothesis |
9 | 2330-2333 | Thus the initial frequency of the light emitted is 6 6 × 1015 Hz It was Niels Bohr (1885 – 1962) who made certain modifications in
this model by adding the ideas of the newly developing quantum
hypothesis Niels Bohr studied in Rutherford’s laboratory for several
months in 1912 and he was convinced about the validity of Rutherford
nuclear model |
9 | 2331-2334 | 6 × 1015 Hz It was Niels Bohr (1885 – 1962) who made certain modifications in
this model by adding the ideas of the newly developing quantum
hypothesis Niels Bohr studied in Rutherford’s laboratory for several
months in 1912 and he was convinced about the validity of Rutherford
nuclear model Faced with the dilemma as discussed above, Bohr, in
1913, concluded that in spite of the success of electromagnetic theory in
explaining large-scale phenomena, it could not be applied to the processes
at the atomic scale |
9 | 2332-2335 | It was Niels Bohr (1885 – 1962) who made certain modifications in
this model by adding the ideas of the newly developing quantum
hypothesis Niels Bohr studied in Rutherford’s laboratory for several
months in 1912 and he was convinced about the validity of Rutherford
nuclear model Faced with the dilemma as discussed above, Bohr, in
1913, concluded that in spite of the success of electromagnetic theory in
explaining large-scale phenomena, it could not be applied to the processes
at the atomic scale It became clear that a fairly radical departure from
the established principles of classical mechanics and electromagnetism
would be needed to understand the structure of atoms and the relation
of atomic structure to atomic spectra |
9 | 2333-2336 | Niels Bohr studied in Rutherford’s laboratory for several
months in 1912 and he was convinced about the validity of Rutherford
nuclear model Faced with the dilemma as discussed above, Bohr, in
1913, concluded that in spite of the success of electromagnetic theory in
explaining large-scale phenomena, it could not be applied to the processes
at the atomic scale It became clear that a fairly radical departure from
the established principles of classical mechanics and electromagnetism
would be needed to understand the structure of atoms and the relation
of atomic structure to atomic spectra Bohr combined classical and early
quantum concepts and gave his theory in the form of three postulates |
9 | 2334-2337 | Faced with the dilemma as discussed above, Bohr, in
1913, concluded that in spite of the success of electromagnetic theory in
explaining large-scale phenomena, it could not be applied to the processes
at the atomic scale It became clear that a fairly radical departure from
the established principles of classical mechanics and electromagnetism
would be needed to understand the structure of atoms and the relation
of atomic structure to atomic spectra Bohr combined classical and early
quantum concepts and gave his theory in the form of three postulates These are :
(i)
Bohr’s first postulate was that an electron in an atom could revolve
in certain stable orbits without the emission of radiant energy,
contrary to the predictions of electromagnetic theory |
9 | 2335-2338 | It became clear that a fairly radical departure from
the established principles of classical mechanics and electromagnetism
would be needed to understand the structure of atoms and the relation
of atomic structure to atomic spectra Bohr combined classical and early
quantum concepts and gave his theory in the form of three postulates These are :
(i)
Bohr’s first postulate was that an electron in an atom could revolve
in certain stable orbits without the emission of radiant energy,
contrary to the predictions of electromagnetic theory According to
this postulate, each atom has certain definite stable states in which it
Rationalised 2023-24
299
Atoms
can exist, and each possible state has definite total energy |
9 | 2336-2339 | Bohr combined classical and early
quantum concepts and gave his theory in the form of three postulates These are :
(i)
Bohr’s first postulate was that an electron in an atom could revolve
in certain stable orbits without the emission of radiant energy,
contrary to the predictions of electromagnetic theory According to
this postulate, each atom has certain definite stable states in which it
Rationalised 2023-24
299
Atoms
can exist, and each possible state has definite total energy These are
called the stationary states of the atom |
9 | 2337-2340 | These are :
(i)
Bohr’s first postulate was that an electron in an atom could revolve
in certain stable orbits without the emission of radiant energy,
contrary to the predictions of electromagnetic theory According to
this postulate, each atom has certain definite stable states in which it
Rationalised 2023-24
299
Atoms
can exist, and each possible state has definite total energy These are
called the stationary states of the atom (ii) Bohr’s second postulate defines these stable orbits |
9 | 2338-2341 | According to
this postulate, each atom has certain definite stable states in which it
Rationalised 2023-24
299
Atoms
can exist, and each possible state has definite total energy These are
called the stationary states of the atom (ii) Bohr’s second postulate defines these stable orbits This postulate
states that the electron revolves around the nucleus only in those
orbits for which the angular momentum is some integral multiple of
h/2p where h is the Planck’s constant (= 6 |
Subsets and Splits