






from numpy import exp, pi, sqrt


def 				__lowerCamelCase     (							__lowerCAmelCase							:					Dict					,							__lowerCAmelCase							:					float = 0.0					,							__lowerCAmelCase							:					float = 1.0							)     ->  int:
   return 1 / sqrt(2 * pi * sigma**2							) * exp(-((x - mu) ** 2) / (2 * sigma**2)							)


if __name__ == "__main__":
       import doctest

       doctest.testmod()











UpperCamelCase    							=      8.3_144_598


def 				__lowerCamelCase     (							__lowerCAmelCase							:					float					,							__lowerCAmelCase							:					float							)     ->  float:
   if temperature < 0:
      raise Exception("""Temperature cannot be less than 0 K"""							)
   if molar_mass <= 0:
      raise Exception("""Molar mass cannot be less than or equal to 0 kg/mol"""							)
   else:
      return (3 * UNIVERSAL_GAS_CONSTANT * temperature / molar_mass) ** 0.5


if __name__ == "__main__":
       import doctest

       # run doctest
       doctest.testmod()

       # example
       UpperCamelCase    							=      300
       UpperCamelCase    							=      28
       UpperCamelCase    							=      rms_speed_of_molecule(temperature, molar_mass)
       print(F"""Vrms of Nitrogen gas at 300 K is {vrms} m/s""")



