Question

At t = 0, number of active nuclei in a sample is N0. How much no. of nuclei will decay in time between its first mean life and second half life?
A
No/e
B
No/e - No/4
C
No/2-No/e
D
No/4

Answer 1

Answer:

B explanation is in the image

Answer 2

The correct option to the above question is (B), which is N₀/e - N₀/4

Given: At t = 0, number of active nuclei = N₀

To find The time between the first mean life and the second half-life.

Solution:

Let the first mean life from decaying from N₀ to N₁ be t₁

and, from N₁ to N₂ be t₂.

t₁ = 1/λ

For N₁, N₁ = N₀e^⁻λt

Putting the value of t₁ into the equation we get,

N₁ = N₀e^⁻λ×1/λ

N₁ = N₀/e

For N₂, N₂ = N₀/2² = N₀/4

Therefore, the number of nuclei that will decay in the time interval between the first mean life and the second half-life = N₁ - N₂

= N₀/e - N₀/4

• The number of nuclei declines to half its original value in one half-life, let t = t1/2 in the exponential in the equation N = N0e−λt.
• One of the most useful terms for estimating how quickly a nuclide will decay is the radioactive half-life (t1/2). The half-life is defined as the amount of time it takes for a given isotope to lose half of its radioactivity.
• The half-life is the time interval for which the radioactive substance decay to its half of the original quantity.