Exams › NEET › Physics

Let the required time be t. Then N1 = N0e^−λ1t ; N2 = N0e^−λ2t Where N1 = number of nuclei of X1 after time t N2 = number of nuclei of X2 after time t N0 = initial number of nuclei of X1 and X2 each.

1. λ1 = 5λ ; N2 = N0e^−λ2t Here N1 = N2 e
2. 1/e = e^−1 ⇒ e^1 = e^4λt ⇒ 4λt = 1
3. t = 1/41
4. None of the above

Correct answer: 1/e = e^−1 ⇒ e^1 = e^4λt ⇒ 4λt = 1

Solution

The equation 1/e = e^(-1) implies that the exponential terms can be equated, leading to 4λt = 1. Solving for t gives t = 1/(4λ). This matches option B.

Related NEET Physics questions

• Two nuclei have their mass numbers in the ratio of 1 : 3. The ratio of their nuclear densities would be:
• If radius of the 27/13 Al nucleus is taken to be R_Al, then the radius of 125/53 Te nucleus is nearly:
• If the nuclear radius of 27/13 Al is 3.6 Fermi, the approximate nuclear radius of 64/29 Cu in Fermi is:
• The radius of germanium (Ge) nuclide is measured to be twice the radius of 9/4 Be. The number of nucleons in Ge are:
• If the nucleus 27/13 Al has nuclear radius of about 3.6 fm, then 125/32 Te would have its radius approximately as:
• The nuclei of which one of the following pairs of nuclei are isobars?

⚔️ Practice NEET Physics free + battle 1v1 →