Welcome to the NCERT Solutions for Class 12th Physics - Chapter Atoms. This page offers a step-by-step solution to the specific question from Exercise 1, Question 9: **a 12 5 ev electron beam is used to bombard gaseous...**.

Question 9

A 12.5 eV electron beam is used to bombard gaseous hydrogen at room temperature. What series of wavelengths will be emitted?

Answer

It is given that the energy of the electron beam used to bombard gaseous hydrogen at room temperature is 12.5 eV.

Also, the energy of the gaseous hydrogen in its ground state at room temperature is −13.6 eV.

When gaseous hydrogen is bombarded with an electron beam, the energy of the gaseous hydrogen becomes −13.6 + 12.5 eV i.e., −1.1 eV.

Orbital energy is related to orbit level (n) as:

E = -13.6/(n)^{2} eV

For n = 3, E = -13.6/(9)^{2} = -1.5 eV

This energy is approximately equal to the energy of gaseous hydrogen. It can be concluded that the electron has jumped from n = 1 to n = 3 level.

During its de-excitation, the electrons can jump from n = 3 to n = 1 directly, which forms a line of the Lyman series of the hydrogen spectrum.

We have the relation for wave number for Lyman series as:

*1/λ = R _{y} (1/1^{2} - 1/n^{2})*

Where,

R_{y} = Rydberg constant = 1.097 × 10^{7} m^{−1}

λ= Wavelength of radiation emitted by the transition of the electron

For n = 3, we can obtain λ as:

1/λ = 1.097 x 10^{7} (1/1^{2} - 1/3^{2})

= 1.097x10^{7}(1-1/9) = 1.097x10^{7}x8/9

λ = 9/(8 x 1.097 x 10^{7}) = 102.55 nm

If the electron jumps from n = 2 to n = 1, then the wavelength of the radiation is given as:

1/λ = 1.097 x 10^{7} (1/1^{2} - 1/2^{2})

= 1.097x10^{7}(1-1/4) = 1.097x10^{7}x3/4

λ = 4/(1.097x10^{7}x3) = 121.54nm

If the transition takes place from n = 3 to n = 2, then the wavelength of the radiation is given as:

1/λ = 1.097 x 10^{7} (1/2^{2} - 1/3^{2})

= 1.097x10^{7}(1/4-1/9) = 1.097x10^{7}x5/36

λ = 36/(5x1.097x10^{7}) = 656.33 nm

This radiation corresponds to the Balmer series of the hydrogen spectrum.

Hence, in Lyman series, two wavelengths i.e., 102.5 nm and 121.5 nm are emitted. And in the Balmer series, one wavelength i.e., 656.33 nm is emitted.

- Q:-
The radius of the innermost electron orbit of a hydrogen atom is 5.3 ×10

^{−11}m. What are the radii of the n = 2 and n =3 orbits? - Q:-
A hydrogen atom initially in the ground level absorbs a photon, which excites it to the n = 4 level. Determine the wavelength and frequency of the photon.

- Q:-
A difference of 2.3 eV separates two energy levels in an atom. What is the frequency of radiation emitted when the atom makes a transition from the upper level to the lower level?

- Q:-
In accordance with the Bohr’s model, find the quantum number that characterises the earth’s revolution around the sun in an orbit of radius 1.5 × 10

^{11}m with orbital speed 3 × 10^{4}m/s. (Mass of earth = 6.0 × 10^{24}kg.) - Q:-
(a) Using the Bohr’s model calculate the speed of the electron in a hydrogen atom in the n = 1, 2, and 3 levels.

(b) Calculate the orbital period in each of these levels.

- Q:-
The ground state energy of hydrogen atom is −13.6 eV. What are the kinetic and potential energies of the electron in this state?

- Q:-
What is the shortest wavelength present in the Paschen series of spectral lines?

- Q:-
Suppose you are given a chance to repeat the alpha-particle scattering experiment using a thin sheet of solid hydrogen in place of the gold foil. (Hydrogen is a solid at temperatures below 14 K.) What results do you expect?

- Q:- Choose the correct alternative from the clues given at the end of the each statement:

(a) The size of the atom in Thomsons model is .......... the atomic size in Rutherfords model. (much greater than/no different from/much less than.)

(b) In the ground state of .......... electrons are in stable equilibrium, while in .......... electrons always experience a net force. (Thomsons model/ Rutherfords model.)

(c) A classical atom based on .......... is doomed to collapse. (Thomsons model/ Rutherfords model.)

(d) An atom has a nearly continuous mass distribution in a .......... but has a highly non-uniform mass distribution in .......... (Thomsons model/ Rutherfords model.)

(e) The positively charged part of the atom possesses most of the mass in .......... (Rutherfords model/both the models.)

- Q:-
Answer the following questions regarding earth's magnetism:

(a) A vector needs three quantities for its specification. Name the three independent quantities conventionally used to specify the earth's magnetic field.

(b) The angle of dip at a location in southern India is about 18º.

Would you expect a greater or smaller dip angle in Britain?

(c) If you made a map of magnetic field lines at Melbourne in Australia, would the lines seem to go into the ground or come out of the ground?

(d) In which direction would a compass free to move in the vertical plane point to, if located right on the geomagnetic north or south pole?

(e) The earth's field, it is claimed, roughly approximates the field due to a dipole of magnetic moment 8 x 1022 J T

^{-1 }located at its centre. Check the order of magnitude of this number in some way.(f ) Geologists claim that besides the main magnetic N-S poles, there are several local poles on the earth's surface oriented in different directions. How is such a thing possible at all?

- Q:-
(a) Two stable isotopes of lithium 6Li3 and7Li3 have respective abundances of 7.5% and 92.5%. These isotopes have masses 6.01512 u and 7.01600 u, respectively. Find the atomic mass of lithium.

(b) Boron has two stable isotopes,

^{10}B_{5}and^{11}B_{5}. Their respective masses are 10.01294 u and 11.00931 u, and the atomic mass of boron is 10.811 u. Find the abundances of^{10}B_{5}and^{11}B_{5}. - Q:-
A small candle, 2.5 cm in size is placed at 27 cm in front of a concave mirror of radius of curvature 36 cm. At what distance from the mirror should a screen be placed in order to obtain a sharp image? Describe the nature and size of the image. If the candle is moved closer to the mirror, how would the screen have to be moved?

- Q:-
Figure 8.6 shows a capacitor made of two circular plates each of radius 12 cm, and separated by 5.0 cm. The capacitor is being charged by an external source (not shown in the figure). The charging current is constant and equal to 0.15 A.

(a) Calculate the capacitance and the rate of charge of potential difference between the plates.

(b) Obtain the displacement current across the plates.

(c) Is Kirchhoff’s first rule (junction rule) valid at each plate of the capacitor? Explain.

- Q:- The storage battery of a car has an emf of 12 V. If the internal resistance of the battery is 0.4Ω, what is the maximum current that can be drawn from the battery?
- Q:- A circular coil of wire consisting of 100 turns, each of radius 8.0 cm carries a current of 0.40 A. What is the magnitude of the magnetic field B at the centre of the coil?
- Q:- A rectangular wire loop of sides 8 cm and 2 cm with a small cut is moving out of a region of uniform magnetic field of magnitude 0.3 T directed normal to the loop. What is the emf developed across the cut if the velocity of the loop is 1 cm s−1 in a direction normal to the

(a) longer side,

(b) shorter side of the loop? For how long does the induced voltage last in each case? - Q:- A 100 Ω resistor is connected to a 220 V, 50 Hz ac supply.

(a) What is the rms value of current in the circuit?

(b) What is the net power consumed over a full cycle? - Q:-
What is the force between two small charged spheres having charges of 2 x 10

^{-7}C and 3 x 10^{-7}C placed 30 cm apart in air? - Q:-
Monochromatic light of wavelength 589 nm is incident from air on a water surface. What are the wavelength, frequency and speed of

(a) reflected, and

(b) refracted light? Refractive index of water is 1.33.

- Q:-
A battery of emf 10 V and internal resistance 3 Ω is connected to a resistor. If the current in the circuit is 0.5 A, what is the resistance of the resistor? What is the terminal voltage of the battery when the circuit is closed?

- Q:- Two charges 2 μC and −2 μC are placed at points A and B 6 cm apart.

(a) Identify an equipotential surface of the system.

(b) What is the direction of the electric field at every point on this surface? - Q:-
Two point charges q

_{A}= 3 μC and q_{B}= −3 μC are located 20 cm apart in vacuum.(a) What is the electric field at the midpoint O of the line AB joining the two charges?

(b) If a negative test charge of magnitude 1.5 × 10

^{−9}C is placed at this point, what is the force experienced by the test charge? - Q:-
Two charges

*-q*and*+q*are located at points (0, 0, -*a*) and (0, 0,*a*), respectively.(a) What is the electrostatic potential at the points?

(b) Obtain the dependence of potential on the distance r of a point from the origin when

*r/a*>> 1.(c) How much work is done in moving a small test charge from the point (5, 0, 0) to (-7, 0, 0) along the x-axis? Does the answer change if the path of the test charge between the same points is not along the x-axis?

- Q:-
A 4 µF capacitor is charged by a 200 V supply. It is then disconnected from the supply, and is connected to another uncharged 2 µF capacitor. How much electrostatic energy of the first capacitor is lost in the form of heat and electromagnetic radiation?

- Q:-
A magnetic dipole is under the influence of two magnetic fields. The angle between the field directions is 60º, and one of the fields has a magnitude of 1.2 x 10

^{-2}T. If the dipole comes to stable equilibrium at an angle of 15º with this field, what is the magnitude of the other field? - Q:-
An infinite line charge produces a field of 9 × 10

^{4}N/C at a distance of 2 cm. Calculate the linear charge density. - Q:-
Two charged conducting spheres of radii

*a*and*b*are connected to each other by a wire. What is the ratio of electric fields at the surfaces of the two spheres? Use the result obtained to explain why charge density on the sharp and pointed ends of a conductor is higher than on its flatter portions. - Q:-
**(a)**An electrostatic field line is a continuous curve. That is, a field line cannot have sudden breaks. Why not?**(b)**Explain why two field lines never cross each other at any point? - Q:-
(a) Three resistors 1 Ω, 2 Ω, and 3 Ω are combined in series. What is the total resistance of the combination?

(b) If the combination is connected to a battery of emf 12 V and negligible internal resistance, obtain the potential drop across each resistor.

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