JEE Main 2021 (Online) 27th July Morning Shift | Atoms and Nuclei Question 176 | Physics

If 'f' denotes the ratio of the number of nuclei decayed (N_d) to the number of nuclei at t = 0 (N₀) then for a collection of radioactive nuclei, the rate of change of 'f' with respect to time is given as :

[$$\lambda$$ is the radioactive decay constant]

$$-$$ $$\lambda$$ (1 $$-$$ e^{$$-$$$$\lambda$$t})

$$\lambda$$ (1 $$-$$ e^{$$-$$$$\lambda$$t})

$$\lambda$$e^{$$-$$$$\lambda$$t}

$$-$$ $$\lambda$$e^{$$-$$$$\lambda$$t}

JEE Main 2021 (Online) 25th July Morning Shift

MCQ (Single Correct Answer)

-1

Out of Syllabus

Some nuclei of a radioactive material are undergoing radioactive decay. The time gap between the instances when a quarter of the nuclei have decayed and when half of the nuclei have decayed is given as :

(where $$\lambda$$ is the decay constant)

$${1 \over 2}{{\ln 2} \over \lambda }$$

$${{\ln 2} \over \lambda }$$

$${{2\ln 2} \over \lambda }$$

$${{\ln {3 \over 2}} \over \lambda }$$

JEE Main 2021 (Online) 25th July Morning Shift

MCQ (Single Correct Answer)

-1

Out of Syllabus

The half-life of $${}^{198}Au$$ is 3 days. If atomic weight of $${}^{198}Au$$ is 198 g/mol then the activity of 2 mg of $${}^{198}Au$$ is [in disintegration/second] :

2.67 $$\times$$ 10¹²

6.06 $$\times$$ 10¹⁸

32.36 $$\times$$ 10¹²

16.18 $$\times$$ 10¹²

JEE Main 2021 (Online) 22th July Evening Shift

MCQ (Single Correct Answer)

-1

A nucleus with mass number 184 initially at rest emits an $$\alpha$$-particle. If the Q value of the reaction is 5.5 MeV, calculate the kinetic energy of the $$\alpha$$-particle.

5.5 MeV

5.0 MeV

5.38 MeV

0.12 MeV

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