1
JEE Main 2023 (Online) 6th April Evening Shift
Numerical
+4
-1

Experimentally it is found that $$12.8 ~\mathrm{eV}$$ energy is required to separate a hydrogen atom into a proton and an electron. So the orbital radius of the electron in a hydrogen atom is $$\frac{9}{x} \times 10^{-10} \mathrm{~m}$$. The value of the $$x$$ is __________.

$$\left(1 \mathrm{eV}=1.6 \times 10^{-19} \mathrm{~J}, \frac{1}{4 \pi \epsilon_{0}}=9 \times 10^{9} \mathrm{Nm}^{2} / \mathrm{C}^{2}\right.$$ and electronic charge $$\left.=1.6 \times 10^{-19} \mathrm{C}\right)$$

2
JEE Main 2023 (Online) 6th April Morning Shift
Numerical
+4
-1

The radius of fifth orbit of the $$\mathrm{Li}^{++}$$ is __________ $$\times 10^{-12} \mathrm{~m}$$.

Take: radius of hydrogen atom $$= 0.51\,\mathop A\limits^o$$

3
JEE Main 2023 (Online) 1st February Evening Shift
Numerical
+4
-1

Nucleus A having $$Z=17$$ and equal number of protons and neutrons has $$1.2 ~\mathrm{MeV}$$ binding energy per nucleon.

Another nucleus $$\mathrm{B}$$ of $$Z=12$$ has total 26 nucleons and $$1.8 ~\mathrm{MeV}$$ binding energy per nucleons.

The difference of binding energy of $$\mathrm{B}$$ and $$\mathrm{A}$$ will be _____________ $$\mathrm{MeV}$$.

4
JEE Main 2023 (Online) 1st February Morning Shift
Numerical
+4
-1

A light of energy $$12.75 ~\mathrm{eV}$$ is incident on a hydrogen atom in its ground state. The atom absorbs the radiation and reaches to one of its excited states. The angular momentum of the atom in the excited state is $$\frac{x}{\pi} \times 10^{-17} ~\mathrm{eVs}$$. The value of $$x$$ is ___________ (use $$h=4.14 \times 10^{-15} ~\mathrm{eVs}, c=3 \times 10^{8} \mathrm{~ms}^{-1}$$ ).