1
JEE Main 2023 (Online) 8th April Morning Shift
+4
-1

For a nucleus $${ }_{\mathrm{A}}^{\mathrm{A}} \mathrm{X}$$ having mass number $$\mathrm{A}$$ and atomic number $$\mathrm{Z}$$

A. The surface energy per nucleon $$\left(b_{\mathrm{s}}\right)=-a_{1} A^{2 / 3}$$.

B. The Coulomb contribution to the binding energy $$\mathrm{b}_{\mathrm{c}}=-a_{2} \frac{Z(Z-1)}{A^{4 / 3}}$$

C. The volume energy $$\mathrm{b}_{\mathrm{v}}=a_{3} A$$

D. Decrease in the binding energy is proportional to surface area.

E. While estimating the surface energy, it is assumed that each nucleon interacts with 12 nucleons. ( $$a_{1}, a_{2}$$ and $$a_{3}$$ are constants)

Choose the most appropriate answer from the options given below:

A
C, D only
B
B, C, E only
C
B, C only
D
A, B, C, D only
2
JEE Main 2023 (Online) 6th April Evening Shift
+4
-1

A small particle of mass $$m$$ moves in such a way that its potential energy $$U=\frac{1}{2} m ~\omega^{2} r^{2}$$ where $$\omega$$ is constant and $$r$$ is the distance of the particle from origin. Assuming Bohr's quantization of momentum and circular orbit, the radius of $$n^{\text {th }}$$ orbit will be proportional to,

A
$$\sqrt{n}$$
B
$$n^{2}$$
C
$$\frac{1}{n}$$
D
$$n$$
3
JEE Main 2023 (Online) 6th April Morning Shift
+4
-1

The energy levels of an hydrogen atom are shown below. The transition corresponding to emission of shortest wavelength is :

A
A
B
C
C
B
D
D
4
JEE Main 2023 (Online) 1st February Evening Shift
+4
-1

An electron of a hydrogen like atom, having $$Z=4$$, jumps from $$4^{\text {th }}$$ energy state to $$2^{\text {nd }}$$ energy state. The energy released in this process, will be :

(Given Rch = $$13.6~\mathrm{eV}$$)

Where R = Rydberg constant

c = Speed of light in vacuum

h = Planck's constant

A
$$10.5 ~\mathrm{eV}$$
B
$$40.8 ~\mathrm{eV}$$
C
$$13.6 ~\mathrm{eV}$$
D
$$3.4 ~\mathrm{eV}$$
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