Q: If the radius of the 3 rd Bohr's orbit of hydrogen atom is r_3 and the radius of 4^ th Bohr's orbit is r_4. Then:

aligned & r=0.529 n^2 Z Å \\ & r_3=0.529 3^2 1 r_4=0.529 4^2 1 \\ & r_4 r_3 = 4^2 3^2 = 16 9 r_4= 16 r_3 9 aligned

Q: The frequency of radiation emitted when the electron falls from n =4 to n =1 in a hydrogen atom will be (Given : ionization energy of H =2.18 10^ -18 ~J atom ^ -1 and h =6.625 10^ -34 Js )

aligned v &= 1 ~h IE [ 1 n _ 1 ^ 2 - 1 n _ 2 ^ 2 ] \\ &= 2.18 10^ -18 6.625 10^ -34 [ 1 1 - 1 16 ]=3.08 10^ 15 ~s ^ -1 aligned

Question 1

The degeneracy of hydrogen atom that has energy equal to -R_ H 9 is (where, R_ H = Rydberg constant)

Accepted Answer

The energy is given as, E=- R_ H 9 ...(i) We know that, aligned E_n & =- R_ H n^2 ...(ii)\ n^2 & =9 \ n & =3 aligned When n=3, l=0,1,2 (3 s, 3 p, 3 d sub-shells) Orbitals present (i.e., degeneracy), 3 s=1,3 p=3,3 d=5 Total number of orbital present =3+1+5=9

Question 2

If the de-broglie wavelength of a particle of mass (m) is 100 times its velocity. Then, its value in terms of its mass (m) and plank constant (h) is

Accepted Answer

Let the wavelength of given particle =x Velocity (v)= x 100 Using wavelength formula aligned = h m v \ & x = h m ( x 100 ) \ x & = 100 h m x \ x^2 & =100 h m \ x & =10 h m aligned

Question 3

The energy of second orbit of hydrogen atom is -5.45 10^ -19 ~J . What is the energy of first orbit of Li ^ 2+ ion (in J) ?

Accepted Answer

E_n=-13.6 [ z^2 n^2 ] e V E_1=-13.6 [ 3^2 1^2 ] eV =-122.4 eV =-122.4 1.602 10^ -19 ~J =-1.962 10^ -17 ~J

Question 4

A photon of wavelength 3000 Ã… strikes a metal surface. The work function of the metal is 2.13 eV. What is the kinetic energy of the emitted photoelectron? ( h =6.626 10^ -34 Js )

Accepted Answer

=3000 Ã…=3 10^ -7 ~m , =2.13 eV K.E. =h v-h v_0=h v- = h c - = (6.626 10^ -34 3 10^8 ) 3 10^ -7 - (2.13 1.6 10^ -19 ) = 1.98 10^ -25 3 10^ -7 - (3.408 10^ -19 ) = (6.60 10^ -19 )- (3.408 10^ -19 ) =3.192 10^ -19 ~J =2.0 eV

Question 5

A stream of electrons from a heated filament was passed between two charged plates kept at a potential difference V volt. If 'e' and m are charge and mass of an electron, respectively, then the value

Accepted Answer

As electron of charge ' e ' is passed through ' V ' volt, kinetic energy of electron will be eV . Wavelength of electron wave ( )= h 2 m KE =- h 2 m eV h = 2 m eV

Question 6

Observe the given boundary surface diagrams of two orbitals I and II and choose the correct option.

Accepted Answer

In boundary surface diagram (1) the four lobes lie between y and z-axis (d_ y z ) whereas, in boundary surface diagram (2) the four lobes lie on the x and y-axis (d_ x^2-y^2 ).

Question 7

If the radius of the 3 rd Bohr's orbit of hydrogen atom is r_3 and the radius of 4^ th Bohr's orbit is r_4. Then:

Accepted Answer

aligned & r=0.529 n^2 Z Å \ & r_3=0.529 3^2 1 r_4=0.529 4^2 1 \ & r_4 r_3 = 4^2 3^2 = 16 9 r_4= 16 r_3 9 aligned

Question 8

The Bohr orbit radius for the hydrogen atom (n=1) is approximately 0.530 Å. The radius for the first excited state (n=2) orbit is (in Å )

Accepted Answer

Given : Radius of hydrogen atom =0.530 Å, Number of excited state (n)=2 and atomic number of hydrogen atom (Z)=1. We know that the Bohr radius (r)= n^2 Z radius of atom = (2)^2 1 0.530 =4 0.530=2.12 Å

Question 9

The probability density plots of 1 s and 2 s orbitals are given in figure. The density of dots in a region represents the probability density of finding electrons in the region. On the basis of above

Accepted Answer

The probability density of electrons in 2 s orbital first increases then decreases and after that it increases again as distance increases from nucleus.

Question 10

The frequency of radiation emitted when the electron falls from n =4 to n =1 in a hydrogen atom will be (Given : ionization energy of H =2.18 10^ -18 ~J atom ^ -1 and h =6.625 10^ -34 Js )

Accepted Answer

aligned v &= 1 ~h IE [ 1 n _ 1 ^ 2 - 1 n _ 2 ^ 2 ] \ &= 2.18 10^ -18 6.625 10^ -34 [ 1 1 - 1 16 ]=3.08 10^ 15 ~s ^ -1 aligned

Question 11

The difference in the number of unpaired electrons of a metal ion in its high-spin and low-spin octahedral complexes is two. The metal ion is:

Accepted Answer

Answer option index: 2

Question 12

Calculate the wavelength (in nanometer) associated with a proton moving at 1.0 10^ 3 ~ms ^ -1 . (Mass of proton =1.67 10^ -27 ~kg and . h =6.63 10^ -34 Js )

Accepted Answer

aligned &= h m v = 6.63 10^ -34 1.67 10^ -27 1 10^ 3 \ &=3.97 10^ -10 meter =0.397 nanometer 0.40 ~nm aligned

Question 13

What is the maximum wavelength line in the Lyman series of He ^ + ion?

Accepted Answer

1 = RZ ^ 2 [ 1 n _ 1 ^ 2 - 1 n _ 2 ^ 2 ]= R 2^ 2 [ 1 l ^ 2 - 1 2^ 2 ] 3 R ; = 1 3 R

Structure of Atom — Previous Year Questions & Solutions