Q4. The half-life period of a radioactive element 'X' is same as the mean life of another radioactiv

Q: What is the correct answer for CUET UG Physics Q4?

The correct answer is C. The half-life period (T_½) is related to the decay constant (λ) by T_½ = ln(2)/λ ≈ 0.693/λ. The mean life (τ) is given by τ = 1/λ. The problem states that the half-life of X is equal to the mean life of Y: T_½(X) = τ(Y). Substituting the formulas: 0.693/λ_X = 1/λ_Y. Rearranging this gives λ_Y = λ_X / 0.693. Since 1/0.693 ≈ 1.44, we have λ_Y ≈ 1.44 λ_X. This means the decay constant of Y is greater

Q: Q4. The half-life period of a radioactive element 'X' is same as the mean life of another radioactive element Y. Initially both of them have the same no. of atoms, then: A. X and Y have the same…

The correct answer is C. The half-life period (T_½) is related to the decay constant (λ) by T_½ = ln(2)/λ ≈ 0.693/λ. The mean life (τ) is given by τ = 1/λ. The problem states that the half-life of X is equal to the mean life of Y: T_½(X) = τ(Y). Substituting the formulas: 0.693/λ_X = 1/λ_Y. Rearranging this gives λ_Y = λ_X / 0.693. Since 1/0.693 ≈ 1.44, we have λ_Y ≈ 1.44 λ_X. This means the decay constant of Y is greater

Q: What are the options for this CUET UG Physics question?

A. A and B Only · B. A Only · C. C only · D. B and D only

Question

Q4. The half-life period of a radioactive element 'X' is same as the mean life of another radioactive element Y. Initially both of them have the same no. of atoms, then:
A. X and Y have the same decay rate initially.
B. X and Y decay at the same rate always.
C. Y will decay at a faster rate than X.
D. X will decay at a faster rate than Y.
Choose the correct answer from the options given below:
(a) A and B Only
(b) A Only
(c) C only
(d) B and D only

FirstInTest · Accepted Answer

The half-life period (T_½) is related to the decay constant (λ) by T_½ = ln(2)/λ ≈ 0.693/λ. The mean life (τ) is given by τ = 1/λ. The problem states that the half-life of X is equal to the mean life of Y: T_½(X) = τ(Y). Substituting the formulas: 0.693/λ_X = 1/λ_Y. Rearranging this gives λ_Y = λ_X / 0.693. Since 1/0.693 ≈ 1.44, we have λ_Y ≈ 1.44 λ_X. This means the decay constant of Y is greater than that of X (λ_Y > λ_X). A larger decay constant implies a faster decay rate. Therefore, element Y will decay at a faster rate than X. Statement C is correct. Statements A and B are incorrect because their decay constants are different, meaning their decay rates will not be the same. Statement D is incorrect because Y decays faster than X.

Answer

A and B Only

Answer

A Only

Answer

C only

Answer

B and D only

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