1
JEE Main 2022 (Online) 27th July Morning Shift
+4
-1
Out of Syllabus

What is the half-life period of a radioactive material if its activity drops to $$1 / 16^{\text {th }}$$ of its initial value in 30 years?

A
9.5 years
B
8.5 years
C
7.5 years
D
10.5 years
2
JEE Main 2022 (Online) 26th July Evening Shift
+4
-1

A nucleus of mass $$M$$ at rest splits into two parts having masses $$\frac{M^{\prime}}{3}$$ and $${{2M'} \over 3}(M' < M)$$. The ratio of de Broglie wavelength of two parts will be :

A
1 : 2
B
2 : 1
C
1 : 1
D
2 : 3
3
JEE Main 2022 (Online) 26th July Evening Shift
+4
-1
Out of Syllabus

Mass numbers of two nuclei are in the ratio of $$4: 3$$. Their nuclear densities will be in the ratio of

A
4 : 3
B
$$\left(\frac{3}{4}\right)^{\frac{1}{3}}$$
C
1 : 1
D
$$\left(\frac{4}{3}\right)^{\frac{1}{3}}$$
4
JEE Main 2022 (Online) 26th July Morning Shift
+4
-1
Out of Syllabus

The disintegration rate of a certain radioactive sample at any instant is 4250 disintegrations per minute. 10 minutes later, the rate becomes 2250 disintegrations per minute. The approximate decay constant is :

$$\left(\right.$$Take $$\left.\log _{10} 1.88=0.274\right)$$

A
$$0.02 \min ^{-1}$$
B
$$2.7 \min ^{-1}$$
C
$$0.063 \min ^{-1}$$
D
$$6.3 \min ^{-1}$$
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