n α-particles per second are being emitted by N atoms of a radioactive element. The half-life of element will be

Question

n α-particles per second are being emitted by N atoms of a radioactive element. The half-life of element will be (A) (n/N) s (B) (N/n) s (C) (0.693N/n) s (D) (0.693n/N) s

Tardigrade Admin · Accepted Answer

The number of α-particles emitted per second is the decay rate R ∴ n=R =λ N n=(0.693N/T1/2) (∵ decay constant λ=(0.693/T1 /2)) ∴ T1/2 =(0.693 N/n) sec

Q. $n$ $α$ -particles per second are being emitted by $N$ atoms of a radioactive element. The half-life of element will be

$(n / N) s$

$(N / n) s$

$\frac{0.693 N}{n} s$

$\frac{0.693 n}{N} s$

The number of $α$ -particles emitted per second is the decay rate R
$∴ n = R = λ N$
$n = \frac{0.693 N}{T _{1/2}}$
$(∵$ decay constant $λ = \frac{0.693}{T _{1/2}})$
$∴ T_{1/2} = \frac{0.693 N}{n} sec$

Q. n α-particles per second are being emitted by N atoms of a radioactive element. The half-life of element will be

(n/N)s

(N/n)s

n0.693N​s

N0.693n​s