Q26 / 97 · NTA Abhyas (JEE Main) 2020 · Physics · Nuclear Physics

$80 kg$ of a radioactive material reduces to $10 kg$ in $1 h$ . The decay constant of the material is

Correct answer
A
$5.80 \times 10^{- 4} s^{- 1}$
B
$1.16 \times 10^{- 3} s^{- 1}$
C
$2.32 \times 10^{- 3} s^{- 1}$
D
$4.64 \times 10^{- 3} s^{- 1}$

Solution

Fraction of material that remains undecayed

\frac{10}{80} = {(\frac{1}{2})}^{\frac{1 h}{T_{1 / 2}}}

3 = \frac{1 h}{T_{1 / 2}}

or

T_{1 / 2} = \frac{60}{3} \min = 20 \min = 1200 s

Now,

λ = \frac{0.693}{T_{1 / 2}} = \frac{0.693}{1200} = 5.8 \times 10^{- 4} s^{- 1}

Hence, the correct answer is option: 'A'.

More Nuclear Physics Questions

The energy spectrum of β - p a r t i c l e s [number N E as a function of β - energy E ] emitted from a radioactive source is
In a sample initially, there are an equal number of atoms of two radioactive isotopes A and B . 3 days later, the number of atoms of A is tw
A and B are two radioactive substances whose half-lives are 1 and 2 years respectively. Initially, 10 g of A and, 1 g of B is taken. The tim
Some amount of a radioactive substance (half-life = 10 days) is spread inside a room and consequently, the level of radiation becomes 50 tim
A nucleus of mass 20 u emits a γ -photon of 6 M e V . If the emission assume to occur when nucleus is free and rest, then the nucleus will h
How long will a radioactive isotope, whose half-life is T years, take for its activity to reduce to 1 8 th of its initial value?