# Activity of substance after a certain time

1. Oct 26, 2014

### desmond iking

1. The problem statement, all variables and given/known data
A sample consists of 2g of a radioactive element. The molar mass of the element is 67g. If the half life of the element is 78 hours, the activity of the sample after 48 hours is ?

2. Relevant equations

3. The attempt at a solution
d(N)/dt = -λN
(2/67 x 6.02x10^23) (ln 2 )/ (78x 3600) = 4.4x10^16s^-1
A= acitivity
A = A_0 (0.5)^x
= (4.4x10^16) x (0.5)^(48/72)

= 2.7x10^16s^-1

but the ans given is 4.4x10^16s^-1

2. Oct 26, 2014

### haruspex

78, not 72.

3. Oct 26, 2014

### desmond iking

After changing 72 to 78.. Is my ans correct?

4. Oct 26, 2014

### haruspex

You posted that the answer given is 4.4x10^16s^-1, but that, as you showed, is the initial activity.
With the 72 changed to 78 your working looks right to me.

5. Oct 26, 2014

### desmond iking

So the ans given is correct? Or my working is correct?

6. Oct 26, 2014

### haruspex

The answer given is clearly wrong because it is the initial activity. It must be less after 48 hours.

7. Oct 27, 2014

### desmond iking

the ans should be
A = A_0 (0.5)^x
= (4.4x10^16) x (0.5)^(48/78)
= 2.87x10^16 ???

8. Oct 27, 2014

### haruspex

Looks right.

Draft saved Draft deleted

Similar Discussions: Activity of substance after a certain time
{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9053550958633423, "perplexity": 7827.1974092166465}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-09/segments/1518891815812.83/warc/CC-MAIN-20180224132508-20180224152508-00194.warc.gz"}