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

Question

80 kg of a radioactive material reduces to 10 kg in 1 h . The decay constant of the material is (A) 5.80 × 10- 4 s- 1 (B) 1.16 × 10- 3 s- 1 (C) 2.32 × 10- 3 s- 1 (D) 4.64× 10- 3 s- 1

Tardigrade Admin · Accepted Answer

Fraction of material that remains undecayed (10/80)=((1/2))(1 h/T1 / 2) 3=(1 h/T1 / 2) or T1 / 2 = (60/3) min = 20 min =1200s Now, λ =(0.693/T1 / 2)=(0.693/1200)= 5.8 × 10- 4 s- 1

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

$5.80 \times 1 0^{- 4} s^{- 1}$

$1.16 \times 1 0^{- 3} s^{- 1}$

$2.32 \times 1 0^{- 3} s^{- 1}$

$4.64 \times 1 0^{- 3} s^{- 1}$

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, $λ = \frac{0.693}{T _{1/2}} = \frac{0.693}{1200} = 5.8 \times 1 0^{- 4} s^{- 1}$

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

5.80×10−4s−1

1.16×10−3s−1

2.32×10−3s−1

4.64×10−3s−1