Q: A particle of mass m is moving around the origin with a constant force F pulling it towards the origin. If Bohr model is used to describe its motion, the radius r of the n^ th orbit and the particle's

aligned & m v^2 r = F ....(1) \\ & mvr = nh 2 v= nh 2 mr ....(2) aligned From equation (1) aligned & m r ( nh 2 mr )^2= F \\ & n ^2 ~h ^2 4 ^2 mF = r ^3 r ^3 n ^2 \\ & r n ^ 2 / 3 aligned From (2) v n r n n^ 2 / 3 v n^ 1 / 3

Q: De-Broglie wavelength of an electron orbiting in the n=2 state of hydrogen atom is close to (Given Bohr radius =0.052 ~nm )

Given n =2, Z =1 aligned & 2 r = n \\ & 2 (0.052 n ^2 Z )= n aligned On solving =0.67 ~nm

Q: Match List I with List II. array |l|l|l|l| & |c| array c List I \\(Spectral Lines of \ for \ from) array & & |c| array l List II \\(Wavelengths (nm)) array \\ A. & n_2=3 to m_1=2 & I. & 410.2 \\ B. &

Energy difference E= h c aligned & 1 E \\ & ( E)_ 6-2 ( E)_ 5-2 ( E)_ 4-2 ( E)_ 3-2 \\ & _ 6-2 _ 5-2 _ 4-2 _ 3-2 aligned A-III, B-IV, C-II, D-I

Question 1

In the first excited state of hydrogen atom, the energy of its electron is -3.4 eV. The radial distance of the electron from the hydrogen nucleus in this case is approximately : (Take 1 eV = 1.6 10^ -

Accepted Answer

The total energy of an electron in a hydrogen atom is given by E = - 1 4 _0 e^2 2r Substituting the given values: -3.4 1.6 10^ -19 = - 9 10^9 (1.6 10^ -19 )^2 2r r = 9 10^9 1.6 10^ -19 2 3.4 r = 14.4 10^ -10 6.8 r 2.117 10^ -10 m This is approximately 2.1 10^ -10 m. Answer: 2.1 10^ -10 m

Question 2

Consider that an electron is revolving in an excited state of Hydrogen atom with velocity 25.6 10^5 ms^ -1 . The radius of the orbit is x 10^ -9 m. The value of x is : [Take the mass of electron to be

Accepted Answer

The electrostatic force between the nucleus and the electron provides the necessary centripetal force for the electron to revolve in its orbit. mv^2 r = 1 4 _0 e^2 r^2 Rearranging for the radius r: r = 1 4 _0 e^2 mv^2 Substituting the given values: 1 4 _0 = 9 10^9 N m^2 C^ -2 e = 1.6 10^ -19 C m = 9 10^ -31 kg v = 25.6 10^5 m s^ -1 r = 9 10^9 (1.6 10^ -19 )^2 9 10^ -31 ( 25.6 10^5)^2 r = 9 10^9 2.56 10^ -38 9 10^ -31 25.6 10^ 10 r = 2.56 10^ -29 25.6 10^ -21 r = 0.1 10^ -8 m r = 1 10^ -9 m Compa

Question 3

In Geiger-Marsden experiment, the number of scattered -particles N( ) is plotted as a function of scattering angle . Which of the following options represents the correct plot ?

Accepted Answer

In the Geiger-Marsden ( -particle scattering) experiment, the number of -particles scattered at an angle is given by the Rutherford scattering formula: N( ) 1 ^4( /2) From this relation, we can observe the following: 1. For small values of , ( /2) is very small, making N( ) very large. Most -particles pass through with very little deflection. 2. As the scattering angle increases, ( /2) increases, causing the number of scattered particles N( ) to decrease rapidly. 3. The minimum number of scatter

Question 4

A particle of mass m is moving around the origin with a constant force F pulling it towards the origin. If Bohr model is used to describe its motion, the radius r of the n^ th orbit and the particle's

Accepted Answer

aligned & m v^2 r = F ....(1) \ & mvr = nh 2 v= nh 2 mr ....(2) aligned From equation (1) aligned & m r ( nh 2 mr )^2= F \ & n ^2 ~h ^2 4 ^2 mF = r ^3 r ^3 n ^2 \ & r n ^ 2 / 3 aligned From (2) v n r n n^ 2 / 3 v n^ 1 / 3

Question 5

De-Broglie wavelength of an electron orbiting in the n=2 state of hydrogen atom is close to (Given Bohr radius =0.052 ~nm )

Accepted Answer

Given n =2, Z =1 aligned & 2 r = n \ & 2 (0.052 n ^2 Z )= n aligned On solving =0.67 ~nm

Question 6

Given below are two statements: Statement I: Atoms are electrically neutral as they contain equal number of positive and negative charges. Statement II: Atoms of each element are stable and emit their

Accepted Answer

Statement I is true as atoms are electrically neutral because they contain equal number of positive and negative charges. Statement II is wrong as atom of most of the elements are stable and emit characteristic spectrum. But this statement is not true for every atom.

Question 7

Some energy levels of a molecule are shown in the figure with their wavelengths of transitions. Then:

Accepted Answer

h c _1 = -5 E 2 +4 E= 3 2 E...(i) h c _2 =-2 E+3 E=E...(ii) h C _3 =-2 E+4 E=2 E...(iii) Comparing (2) and (3) 1 _3 = 2 _2 _2=2 _3 Comparing (1) and (2) 3 _1=2 _2 _1 _2

Question 8

Match List I with List II. array |l|l|l|l| & |c| array c List I \(Spectral Lines of \ for \ from) array & & |c| array l List II \(Wavelengths (nm)) array \ A. & n_2=3 to m_1=2 & I. & 410.2 \ B. &

Accepted Answer

Energy difference E= h c aligned & 1 E \ & ( E)_ 6-2 ( E)_ 5-2 ( E)_ 4-2 ( E)_ 3-2 \ & _ 6-2 _ 5-2 _ 4-2 _ 3-2 aligned A-III, B-IV, C-II, D-I

Question 9

The spectral series which corresponds to the electronic transition from the levels n_2=5,6, to the level n_1=4 is

Accepted Answer

The spectral series which corresponds to the electronic transition from the levels n_2=5,6, to n_1=4 is Brackett series.

Atomic Physics — Previous Year Questions & Solutions