The decay constant for ^ 238 U is 4.9 × 10^ -18 s^ -1 . Determine the average-life of ^ 238 U .

Correct answer: C. 6.49 × 10^ 9 y The decay constant is given as λ = 4.9 × 10^ -18 s^ -1 . The average life is the reciprocal of the decay constant: = (1)/(λ) = 1 4.9 × 10^ -18 s = 2.04 × 10^ 17 s Converting seconds to years (using 1 year 3.14 × 10^7 s ): = 2.04 × 10^ 17 3.14 × 10^7 y 6.49 × 10^9 y

Concepts Of Physics MCQ Edition [Volume 2]

Exam: Concepts Of Physics MCQ Edition [Volume 2]
Subject: Physics
Chapter: The Nucleus

Concepts Of Physics MCQ Edition [Volume 2] · Physics · The Nucleus

The decay constant for ^ 238 U is 4.9 × 10^ -18 s^ -1 . Determine...

The decay constant for ^{238}\text{U}

is

4.9 \times 10^{-18} \text{ s}^{-1}

. Determine the average-life of ^{238}\text{U}

Options

A $3.15 \times 10^{7} \text{ y}$
B $2.04 \times 10^{17} \text{ y}$
C $6.49 \times 10^{9} \text{ y}$
D $4.50 \times 10^{9} \text{ y}$

Correct answer

C. $6.49 \times 10^{9} \text{ y}$

Step-by-step solution

The decay constant is given as

\lambda = 4.9 \times 10^{-18} \text{ s}^{-1}

.

The average life

\tau

is the reciprocal of the decay constant:

\tau = \dfrac{1}{\lambda} = \dfrac{1}{4.9 \times 10^{-18}} \text{ s} = 2.04 \times 10^{17} \text{ s}

Converting seconds to years (using

1 \text{ year} \approx 3.14 \times 10^7 \text{ s}

\tau = \dfrac{2.04 \times 10^{17}}{3.14 \times 10^7} \text{ y} \approx 6.49 \times 10^9 \text{ y}

Practice The Nucleus on Quantrex Academy →

More from The Nucleus