Let N_{\beta } be the number of \beta particles emitted by 1 gram of Na 24 radioactive nuclei

(half life=15 hrs) in 7.5 hours, N_{\beta } is close to (Avogadro number =6.023\times1023/g. mole) :

 

  • Option 1)

    6.2\times 10^{21}

  • Option 2)

    7.5\times 10^{21}

  • Option 3)

    1.25\times 10^{22}

  • Option 4)

    1.75\times 10^{22}

 

Answers (1)

As we learnt in

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

 

 Total number of nuclei in 

1 g of Na^{24}=\frac{1}{24}\times6.02\times10^{23}=2.5\times 10^{22}=N_{0}

Number of nuclei left after 7.5 hr is

N=\frac{N_{0}}{2^{t/T_{1/2}}}=\frac{2.5\times 10^{22}}{2^{7.5/15}}=\frac{2.5\times 10^{22}}{2^{1/2}}=1.75\times 10^{22}

Correct option is 4.


Option 1)

6.2\times 10^{21}

This is an incorrect option.

Option 2)

7.5\times 10^{21}

This is the correct option.

Option 3)

1.25\times 10^{22}

This is an incorrect option.

Option 4)

1.75\times 10^{22}

This is an incorrect option.

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