Atoms

Previous Years' CBSE Board Questions

12.2 Alpha-Particle Scattering and Rutherford's Nuclear Model of Atom

MCO

1. Which of the following statements is not correct according to Rutherford model?
2. Most of the space inside an atom is empty.
3. The stability of atom was established by the model. (2020) R
4. The electrons revolve around the nucleus under the influence of coulomb force acting on them.
5. Most part of the mass of the atom and its positive charge are concentrated at its centre.

SAI (2 marks)

1. In Geiger-Marsden experiment, the distance of closest approach is considerably larger than the sum of the radii of the gold nucleus and the <math>\alpha</math>-particle. Explain.
2. The total energy of hydrogen atom in a state is -3.4 eV. What are the kinetic and potential energies of the electron in this state? (2022C)
3. What result do you expect if <math>\alpha</math>-particle scattering experiment is repeated using a thin sheet hydrogen in place of a gold foil? Explain. (Hydrogen is a solid at temperature below 14 K) (Term II 2021-22) [II]
4. In the Geiger-Marsden experiment, an <math>\alpha</math>-particle of 5.12 MeV energy approaches a gold target (Z = 79), comes momentarily to rest and then reverses its direction. Find the distance of closest approach of α-particle to the target nucleus. (2020)

Define the distance of closest approach. An

α-particle of kinetic energy 'K' is bombarded on a

thin gold foil. The distance of the closest approach is

'r'. What will be the distance of closest approach for

an α-particle of double the kinetic energy?

(Delhi 2017) (An

1. Write two important limitations of Rutherford nuclear model of the atom. (Delhi 2017) R
2. Using Rutherford's model of the atom, derive the expression for the total energy of the electron in hydrogen atom. What is the significance of total negative energy possessed by the electron?

(Al 2014) Fu

SA II (3 marks)

(a) The energy of hydrogen atom in an orbit is

-1.51 eV. What are kinetic and potential energies of

the electron in this orbit?

(b) The electron in a hydrogen atom is typically

found at a distance of about 5.3 × 10^-11 m from

the nucleus which has a diameter of about

<math>1.0 \times 10^{-15}</math> m. Assuming the hydrogen atom to be a

sphere of radius 5.3 × 10^-11 m, what fraction of its

volume is occupied by the nucleus.

(Term II 2021-22) (Ev)

(a) In the Geiger-Marsden experiment, find the

distance of closest approach to the gold nucleus

(mass number = 79) of a 7.7 MeV <math>\alpha</math>-particle before

it comes momentarily to rest and reverses its

direction. Why is it different from actual radius of

gold nucleus? (2021)

(b) Plot a graph between number of scattered

α-particles detected in gold foil experiment and

angle of scattering. What is the main assumption in

plotting this graph? (2021C)

1. In Geiger-Marsden scattering experiment, the trajectory of α-particles in Coulomb's field of a heavy nucleus is shown in the figure.

Target nucleus

1. What do b and θ represent in the figure?
2. What will be the value of b for (i) θ = 0°.
3. <math>\theta = 180^{\circ}</math>?

(2020) (i)

LA (5 marks)

1. In Rutherford scattering experiment, draw the trajectory traced by <math>\alpha</math>-particles in the coulomb field of target nucleus and explain how this led to estimate the size of the nucleus.

(3/5, Al 2015C) (An)

12.4 Bohr Model of the Hydrogen Atom

MCO

The radius of the n^th orbit in Bohr model of hydrogen atom is proportional to

1. n² (b) <math>\frac{1}{2}</math> (c) n (d) <math>\frac{1}{n}</math> (2023) U

SAI (2 marks)

Using Bohr's atomic model, derive the expression for the radius of nth orbit of the revolving electron in a hydrogen atom. (2020) An OR Show that the radius of the orbit in hydrogen atom varies as <math>n^2</math>, where n is the principal quantum number of the atom. (Delhi 2015)

(a) In Geiger-Marsden experiment, calculate the

distance of closest approach for an alpha particle

with energy 2,56 × 10^-12 J. Consider that the particle

approaches gold nucleus (<math>Z = 79</math>) in head-on position.

(b) If the above experiment is repeated with a

proton of the same energy, then what will be the

value of the distance of closest approach?

(Term II 2021-22)

Draw a graph showing the variation of number of

particles scattered (N) with the scattering angle 0

in Geiger-Marsden experiment. Why only a small

fraction of the particles are scattered at <math>\theta > 90^{\circ}</math>?

Mention two limitations of Rutherford nuclear

model of an atom. (Term II 2021-22)

1. Explain briefly how Rutherford scattering of α-particle by a target nucleus can provide information of the size of the nucleus. (2/3, Delhi 2019) (U
2. the minimum wavelength in Balmer series of hydrogen spectrum. (2022C)
3. Using Bohr's postulates, derive the expression for the orbital period of the electron moving in the nth orbit of hydrogen atom. (2/3, Al 2019) III
4. A hydrogen atom initially in the ground state absorbs a photon which excites it to the <math>n = 4</math> level. Estimate the frequency of the photon. (1/3, 2018)

(a) The radius of the innermost electron orbit of a

hydrogen atom is <math>5.3 \times 10^{-11}</math> m. Calculate its radius

in <math>n = 3</math> orbit. (b) The total energy of an electron in the first

excited state of the hydrogen atom is 3.4 eV. Find

out its (i) kinetic energy and (ii) potential energy in

this state. (Delhi 2014C) Ev

LA (5 marks)

1. (a) Write two important limitations of Rutherford model which could not explain the observed features of atomic spectra. How were these explained in Bohr's model of hydrogen atom?
2. Using Bohr's postulates, obtain the expression for the radius of the <math>n^{th}</math> orbit in hydrogen atom.

OR (4/5, Delhi 2015C) [An]