Science (English Medium) कक्षा १२ - CBSE Question Bank Solutions

In many experimental set-ups the source and screen are fixed at a distance say D and the lens is movable. Show that there are two positions for the lens for which an image is formed on the screen. Find the distance between these points and the ratio of the image sizes for these two points.

The binding energy of a H-atom, considering an electron moving around a fixed nuclei (proton), is B = `- (Me^4)/(8n^2ε_0^2h^2)`. (m = electron mass). If one decides to work in a frame of reference where the electron is at rest, the proton would be moving around it. By similar arguments, the binding energy would be

B = `- (Me^4)/(8n^2ε_0^2h^2)` (M = proton mass)

This last expression is not correct because ______.

The simple Bohr model cannot be directly applied to calculate the energy levels of an atom with many electrons. This is because ______.

For the ground state, the electron in the H-atom has an angular momentum = h, according to the simple Bohr model. Angular momentum is a vector and hence there will be infinitely many orbits with the vector pointing in all possible directions. In actuality, this is not true ______.

A set of atoms in an excited state decays ______.

An ionised H-molecule consists of an electron and two protons. The protons are separated by a small distance of the order of angstrom. In the ground state ______.

1. the electron would not move in circular orbits.
2. the energy would be (2)⁴ times that of a H-atom.
3. the electrons, orbit would go around the protons.
4. the molecule will soon decay in a proton and a H-atom.

Consider aiming a beam of free electrons towards free protons. When they scatter, an electron and a proton cannot combine to produce a H-atom ______.

1. because of energy conservation.
2. without simultaneously releasing energy in the from of radiation.
3. because of momentum conservation.
4. because of angular momentum conservation.

The Bohr model for the spectra of a H-atom ______.

1. will not be applicable to hydrogen in the molecular from.
2. will not be applicable as it is for a He-atom.
3. is valid only at room temperature.
4. predicts continuous as well as discrete spectral lines.

Taking the Bohr radius as a₀ = 53 pm, the radius of Li⁺⁺ ion in its ground state, on the basis of Bohr’s model, will be about ______.

The mass of a H-atom is less than the sum of the masses of a proton and electron. Why is this?

When an electron falls from a higher energy to a lower energy level, the difference in the energies appears in the form of electromagnetic radiation. Why cannot it be emitted as other forms of energy?

Using Bohr model, calculate the electric current created by the electron when the H-atom is in the ground state.

If a proton had a radius R and the charge was uniformly distributed, calculate using Bohr theory, the ground state energy of a H-atom when (i) R = 0.1 Å, and (ii) R = 10 Å.

The inverse square law in electrostatics is |F| = `e^2/((4πε_0).r^2)` for the force between an electron and a proton. The `(1/r)` dependence of |F| can be understood in quantum theory as being due to the fact that the ‘particle’ of light (photon) is massless. If photons had a mass m_p, force would be modified to |F| = `e^2/((4πε_0)r^2) [1/r^2 + λ/r]`, exp (– λr) where λ = m_pc/h and h = `h/(2π)`. Estimate the change in the ground state energy of a H-atom if m_p were 10^-6 times the mass of an electron.

M_x and M_y denote the atomic masses of the parent and the daughter nuclei respectively in a radioactive decay. The Q-value for a β^– decay is Q₁ and that for a β⁺ decay is Q₂. If m e denotes the mass of an electron, then which of the following statements is correct?

Tritium is an isotope of hydrogen whose nucleus Triton contains 2 neutrons and 1 proton. Free neutrons decay into `p + bare + barν`. If one of the neutrons in Triton decays, it would transform into He³ nucleus. This does not happen. This is because ______.

Heavy stable nucle have more neutrons than protons. This is because of the fact that ______.

He₂³ and He₁³ nuclei have the same mass number. Do they have the same binding energy?

The deuteron is bound by nuclear forces just as H-atom is made up of p and e bound by electrostatic forces. If we consider the force between neutron and proton in deuteron as given in the form of a Coulomb potential but with an effective charge e′: F = `1/(4πε_0) e^('2)/r` estimate the value of (e’/e) given that the binding energy of a deuteron is 2.2 MeV.

Nuclei with magic no. of proton Z = 2, 8, 20, 28, 50, 52 and magic no. of neutrons N = 2, 8, 20, 28, 50, 82 and 126 are found to be very stable.

(i) Verify this by calculating the proton separation energy S_p for ¹²⁰Sn (Z = 50) and ¹²¹Sb = (Z = 51).

The proton separation energy for a nuclide is the minimum energy required to separate the least tightly bound proton from a nucleus of that nuclide. It is given by `S_P = (M_(z-1^' N) + M_H - M_(ZN))c^2`. 

Given ¹¹⁹In = 118.9058u, ¹²⁰Sn = 119.902199u, ¹²¹Sb = 120.903824u, ¹H = 1.0078252u.

(ii) What does the existance of magic number indicate?