JEE Main 2017 · 2 Apr · Shift 1 · Physics Q26

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PhysicsSingle correct+4 / -1Question 26 of 90

A radioactive nucleus A with a half life T, decays into a nucleus B. At t = 0, there is no nucleus B. At sometime t, the ratio of the number of B to that of A is 0.3. Then, t is given by :

t=\dfrac T2\,\dfrac{\log2}{\log1.3}

t=T\,\dfrac{\log1.3}{\log2}

t=T\log(1.3)

t=\dfrac T{\log(1.3)}

Answer and worked solution

Official answer: B

$\dfrac{N_B}{N_A}=2^{t/T}-1=0.3$ , so $2^{t/T}=1.3$ and
$t=T\frac{\log1.3}{\log2}.$

Topics:Radioactive decay

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JEE Main 2017 · 2 Apr · Shift 1, Physics question 26