The activity of a freshly prepared radioactive sample is 1010 disintegrations per second, whose mean life is 109 s. The mass of an atom of this radioisotope is 10-25 kg. The mass (in mg ) of the radioactive sample is

Question

The activity of a freshly prepared radioactive sample is 1010 disintegrations per second, whose mean life is 109 s. The mass of an atom of this radioisotope is 10-25 kg. The mass (in mg ) of the radioactive sample is (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

( dN / dt )=λ N ∴ N =((( d N / dt ))/λ)=1010 × 10°=1019 atoms m text sample =10-25 × 1019 kg =1 mg

Q. The activity of a freshly prepared radioactive sample is $1 0^{10}$ disintegrations per second, whose mean life is $1 0^{9} s$ . The mass of an atom of this radioisotope is $1 0^{- 25} k g$ . The mass (in $m g$ ) of the radioactive sample is

$\frac{d N}{d t} = λ N$
$∴ N = \frac{( \frac{d N}{d t} )}{λ} = 1 0^{10} \times 1 0^{\circ} = 1 0^{19}$ atoms
$m_{sample = 10}^{- 25} \times 1 0^{19} k g = 1 m g$

Q. The activity of a freshly prepared radioactive sample is 1010 disintegrations per second, whose mean life is 109s. The mass of an atom of this radioisotope is 10−25kg. The mass (in mg ) of the radioactive sample is

dtdN​=λN ∴N=λ(dtdN​)​=1010×10∘=1019 atoms msample =10−25​×1019kg=1mg

Q. The activity of a freshly prepared radioactive sample is $1 0^{10}$ disintegrations per second, whose mean life is $1 0^{9} s$ . The mass of an atom of this radioisotope is $1 0^{- 25} k g$ . The mass (in $m g$ ) of the radioactive sample is

$\frac{d N}{d t} = λ N$
$∴ N = \frac{( \frac{d N}{d t} )}{λ} = 1 0^{10} \times 1 0^{\circ} = 1 0^{19}$ atoms
$m_{sample = 10}^{- 25} \times 1 0^{19} k g = 1 m g$