1
JEE Main 2023 (Online) 15th April Morning Shift
Numerical
+4
-1
As per given figure $A, B$ and $C$ are the first, second and third excited energy levels of hydrogen atom respectively. If the ratio of the two wavelengths $\left(\right.$ i.e. $\left.\frac{\lambda_{1}}{\lambda_{2}}\right)$ is $\frac{7}{4 n}$, then the value of $n$ will be __________.

2
JEE Main 2023 (Online) 13th April Morning Shift
Numerical
+4
-1

The radius of $$2^{\text {nd }}$$ orbit of $$\mathrm{He}^{+}$$ of Bohr's model is $$r_{1}$$ and that of fourth orbit of $$\mathrm{Be}^{3+}$$ is represented as $$r_{2}$$. Now the ratio $$\frac{r_{2}}{r_{1}}$$ is $$x: 1$$. The value of $$x$$ is ___________.

3
JEE Main 2023 (Online) 12th April Morning Shift
Numerical
+4
-1

A common example of alpha decay is $${ }_{92}^{238} \mathrm{U} \longrightarrow{ }_{90}^{234} \mathrm{Th}+{ }_{2} \mathrm{He}^{4}+\mathrm{Q}$$

Given :

$${ }_{92}^{238} \mathrm{U}=238.05060 ~\mathrm{u}$$,

$${ }_{90}^{234} \mathrm{Th}=234.04360 ~\mathrm{u}$$,

$${ }_{2}^{4} \mathrm{He}=4.00260 ~\mathrm{u}$$ and

$$1 \mathrm{u}=931.5 \frac{\mathrm{MeV}}{c^{2}}$$

The energy released $$(Q)$$ during the alpha decay of $${ }_{92}^{238} \mathrm{U}$$ is __________ MeV

4
JEE Main 2023 (Online) 11th April Evening Shift
Numerical
+4
-1

A nucleus disintegrates into two nuclear parts, in such a way that ratio of their nuclear sizes is $$1: 2^{1 / 3}$$. Their respective speed have a ratio of $$n: 1$$. The value of $n$ is __________.

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