Q18. The half-life of a radioactive substance is 10 days. How many days will it take to disintegrate

Q: What is the correct answer for CUET UG Physics Q18?

The correct answer is c. The amount of a radioactive substance remaining (N) after time t is given by the formula N = N₀ * (1/2)^(t/T_½), where N₀ is the initial amount, and T_½ is the half-life. We are given that the half-life (T_½) is 10 days. The substance needs to disintegrate 3/4 of its initial value, which means the remaining amount is N = N₀ - (3/4)N₀ = (1/4)N₀. Substituting these into the decay formula: (1/4)N₀ =

Q: Q18. The half-life of a radioactive substance is 10 days. How many days will it take to disintegrate 3/4 of its initial value? (a) 5 days (b) 10 days (c) 20 days (d) 15 days

The correct answer is c. The amount of a radioactive substance remaining (N) after time t is given by the formula N = N₀ * (1/2)^(t/T_½), where N₀ is the initial amount, and T_½ is the half-life. We are given that the half-life (T_½) is 10 days. The substance needs to disintegrate 3/4 of its initial value, which means the remaining amount is N = N₀ - (3/4)N₀ = (1/4)N₀. Substituting these into the decay formula: (1/4)N₀ =

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

A. 5 days · B. 10 days · C. 20 days · D. 15 days

Question

Q18. The half-life of a radioactive substance is 10 days. How many days will it take to disintegrate 3/4 of its initial value?
(a) 5 days
(b) 10 days
(c) 20 days
(d) 15 days

FirstInTest · Accepted Answer

The amount of a radioactive substance remaining (N) after time t is given by the formula N = N₀ * (1/2)^(t/T_½), where N₀ is the initial amount, and T_½ is the half-life. We are given that the half-life (T_½) is 10 days. The substance needs to disintegrate 3/4 of its initial value, which means the remaining amount is N = N₀ - (3/4)N₀ = (1/4)N₀. Substituting these into the decay formula: (1/4)N₀ = N₀ * (1/2)^(t/10). This simplifies to 1/4 = (1/2)^(t/10). Since 1/4 can be written as (1/2)², we have (1/2)² = (1/2)^(t/10). Equating the exponents, 2 = t/10. Solving for t, we get t = 2 * 10 = 20 days. Therefore, it will take 20 days for 3/4 of the substance to disintegrate. Options (a), (b), and (d) are incorrect time durations.

Answer

5 days

Answer

10 days

Answer

20 days

Answer

15 days

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