Cobalt-57 is radioactive, emitting β -particles. The half-life for this is 270 days. If 100 mg of this is kept in an open container, then what mass (in mg ) of Cobalt-57 will remain after 540 days?

Question

Cobalt-57 is radioactive, emitting β -particles. The half-life for this is 270 days. If 100 mg of this is kept in an open container, then what mass (in mg ) of Cobalt-57 will remain after 540 days? (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

Here, T(1/2)=270 days. After 540 days, it means two half lives have been completed i.e., n=2 If (N/N0)=((1/2))n ⇒ (m/m0)=((1/2))n [ ∵ from Equation. (i)] ⇒ (m/100)=(1/4) ⇒ m=25 mg

Q. Cobalt-57 is radioactive, emitting $β$ -particles. The half-life for this is $270$ days. If $100 m g$ of this is kept in an open container, then what mass (in $m g$ ) of Cobalt-57 will remain after $540$ days?

Here, $T_{\frac{1}{2}} = 270$ days.
After $540$ days, it means two half lives have been completed i.e., $n = 2$
If $\frac{N}{N _{0}} = (\frac{1}{2})^{n}$
$\Rightarrow \frac{m}{m _{0}} = (\frac{1}{2})^{n}$ [ $∵$ from Equation. (i)]
$\Rightarrow \frac{m}{100} = \frac{1}{4}$
$\Rightarrow m = 25 m g$

Q. Cobalt-57 is radioactive, emitting β -particles. The half-life for this is 270 days. If 100mg of this is kept in an open container, then what mass (in mg ) of Cobalt-57 will remain after 540 days?

Here, T21​​=270 days. After 540 days, it means two half lives have been completed i.e., n=2 If N0​N​=(21​)n ⇒m0​m​=(21​)n [ ∵ from Equation. (i)] ⇒100m​=41​ ⇒m=25mg

Q. Cobalt-57 is radioactive, emitting $β$ -particles. The half-life for this is $270$ days. If $100 m g$ of this is kept in an open container, then what mass (in $m g$ ) of Cobalt-57 will remain after $540$ days?

Here, $T_{\frac{1}{2}} = 270$ days.
After $540$ days, it means two half lives have been completed i.e., $n = 2$
If $\frac{N}{N _{0}} = (\frac{1}{2})^{n}$
$\Rightarrow \frac{m}{m _{0}} = (\frac{1}{2})^{n}$ [ $∵$ from Equation. (i)]
$\Rightarrow \frac{m}{100} = \frac{1}{4}$
$\Rightarrow m = 25 m g$