An isotope decays to 1 / 16 th of its mass in 1 h . What is the half-life period of the isotope?

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Question: Answered & Verified by Expert

An isotope decays to

1 / 16^{th}

of its mass in

1 h .

What is the half-life period of the isotope?

PhysicsNuclear PhysicsNEET

Options:

A $15 \min$
B $30 \min$
C $12 \min$
D $10 \min$

Solution:

2739 Upvotes Verified Answer

The correct answer is:

15 \min

N = N_{0} {(\frac{1}{2})}^{n}

\frac{N_{0}}{16} = N_{0} {(\frac{1}{2})}^{n}

{(\frac{1}{2})}^{4} = {(\frac{1}{2})}^{n}

∴

n = 4

\frac{T}{T_{\frac{1}{2}}} = 4

⇒ \frac{1}{T_{\frac{1}{2}}} = 4

⇒ T_{\frac{1}{2}} = \frac{1}{4} h = 15 min

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