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  • Help me solve this Using a nuclear counter the count rate of emitted particles from a radioactive source is measured. At t = 0 it was 1600 counts per second and t=8 seconds it was 100 counts per second. The count rate observed, as counts per second, at t=

Using a nuclear counter the count rate of emitted particles from a radioactive source is measured. At t = 0 it was 1600 counts per second and t=8 seconds it was 100 counts per second. The count rate observed, as counts per second, at t=6 seconds is close to:  

  • Option 1)

    200

  • Option 2)

    150

  • Option 3)

    400

  • Option 4)

    360

Answers (2)

best_answer

 

Number of nuclei in terms of half life -

N=\frac{N_{0}}{2^{t/t_{1/2}}}

- wherein

Very useful to determine number of nuclei in terms of half life

 

let A= count rate of emited particle from radioactive source in count per second.

then

at\: \:\: t=0,A_{0}=1600c/s\\\\at\: \: \: \: t=8, A_{8}=100c/s

 

as we have

 

N=\frac{N_{o}}{2^{(\frac{t}{t_{\frac{1}{2}}})}}

similarly

 

A=\frac{A_{0}}{2(\frac{t}{t_{\frac{1}{2}}})}

 

A_{8}=\frac{A_{0}}{2(\frac{8}{t_{\frac{1}{2}}})}

\frac{A_{0}}{A_{8}}= 2\left ( \frac{8}{t_{\frac{1}{2}}} \right )=\frac{1600}{100}=16=2^{4}\\\\\Rightarrow \frac{8}{t_{\frac{1}{2}}}=4\\\\t_{\frac{1}{2}}=2sec\\\\\: \: so\: \: \: for\: \: t=6 sec\\\\\\A_{6}=\frac{A_{0}}{2\frac{t}{t_{\frac{1}{2}}}}=\frac{A_{0}}{2^{6/2}}=\frac{A_{0}}{2^{3}}=\frac{A_{0}}{8}\\\\\\\\A_{6}=\frac{A_{0}}{8}=\frac{1600}{8}=200c/s\\\\\\A_{6}=200c/s

 

 

 

 


Option 1)

200

Option 2)

150

Option 3)

400

Option 4)

360

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admin

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Number of nuclei in terms of half life -

N=\frac{N_{0}}{2^{t/t_{1/2}}}

- wherein

Very useful to determine number of nuclei in terms of half life

 

let A= count rate of emited particle from radioactive source in count per second.

then

at\: \:\: t=0,A_{0}=1600c/s\\\\at\: \: \: \: t=8, A_{8}=100c/s

 

as we have

 

N=\frac{N_{o}}{2^{(\frac{t}{t_{\frac{1}{2}}})}}

similarly

 

A=\frac{A_{0}}{2(\frac{t}{t_{\frac{1}{2}}})}

 

A_{8}=\frac{A_{0}}{2(\frac{8}{t_{\frac{1}{2}}})}

\frac{A_{0}}{A_{8}}= 2\left ( \frac{8}{t_{\frac{1}{2}}} \right )=\frac{1600}{100}=16=2^{4}\\\\\Rightarrow \frac{8}{t_{\frac{1}{2}}}=4\\\\t_{\frac{1}{2}}=2sec\\\\\: \: so\: \: \: for\: \: t=6 sec\\\\\\A_{6}=\frac{A_{0}}{2\frac{t}{t_{\frac{1}{2}}}}=\frac{A_{0}}{2^{6/2}}=\frac{A_{0}}{2^{3}}=\frac{A_{0}}{8}\\\\\\\\A_{6}=\frac{A_{0}}{8}=\frac{1600}{8}=200c/s\\\\\\A_{6}=200c/s

 

 

 

 

Posted by

Krushnamaya Behera

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