An electron revolves round a nucleus of atomic number Z. If 32.4 eV of energy is required to …

Q. An electron revolves round a nucleus of atomic number Z. If 32.4 eV of energy is required to excite an electron from the n = 3 state to n = 4 state, then the value of Z is

(a) 5

(b) 6

(c)4

(d) 7

Ans: (d)

Sol:E3 = −13.6Z2/32    and E4 = −13.6Z2/42

ΔE = E4 − E3

ΔE = ( −13.6Z2/42)-( −13.6Z2/32)

ΔE = 13.6Z2[1/32 – 1/42]

ΔE = 13.6Z2[7/9×16]

32.4 = 13.6Z2[7/9×16]

Z2 = (32.4 × 9 × 16)/(13.6×7)

Z2 = 49

Z = 7

In a stationary hydrogen atom, an electron jumps from n = 3 to n = 1. The recoil speed of the hydrogen atom is about

Q. In a stationary hydrogen atom, an electron jumps from n = 3 to n = 1. The recoil speed of the hydrogen atom is about

(a) 4 m/s

(b) 4 cm/s

(c)4 mm/s

(d) 4 × 10-4 m/s

Ans: (a)

Sol: 1/λ = R[1/12 − 1/32]

1/ λ = R[1−1/9] = 8R/9

λ = 9/8R   ….(i)

Momentum , P = mv

h/λ = mv

v = h/λm

v = h/(m×9/8R)      ; ( on putting the value of λ from(i))

v = 8Rh/9m

By putting the Standard values of R , h & m we get,

v = 4 m/s

 

The time period of the electron in the ground state of hydrogen atom is two times the time period of the electron…..

Q. The time period of the electron in the ground state of hydrogen atom is two times the time period of the electron in the first excited state of a certain hydrogen like atom (Atomic Number Z). The value of Z is

(a) 2

(b) 3

(c)4

(d) None of these

Ans: (c)

Sol: Time Period ,  T ∝ n3/Z2

Hence , T1/T2 = ( n13/n23 )×(Z22/Z12)

T1/T21/n2 )3 x (Z2/Z1)2

2T2/T23(Z/1)2

16 = Z2

Z = 4

A stationary hydrogen atom emits photon corresponding to the first line of Lyman series. If R is the Rydberg’s constant….

Q. A stationary hydrogen atom emits photon corresponding to the first line of Lyman series. If R is the Rydberg’s constant and M is the mass of the atom, then the velocity acquired by the atom is

(a)     3Rh/4M

(b)      4M/3Rh

(c)      Rh/4M

(d)    4M/Rh

Ans: (a)

Sol: For first Line of Lyman series ,

1/λ = R[1/12 − 1/22] = R[1 −1/4] = 3R/4

Momentum P = h/λ

⇒ Mv = h/λ = h(3R/4)

hence , v = 3Rh/4M

Let An be the area enclosed by the nth orbit in a hydrogen atom. The graph of In (An/A1) against In (n)

Q. Let An be the area enclosed by the nth orbit in a hydrogen atom. The graph of ln (An/A1) against In (n)

(a) will not pass through origin

(b) will be a straight line with slope 4

(c) will be a rectangular hyperbola

(d) will be a parabola

Ans: (b)

Sol: An = π rn2

An = π(r0n2)2

Hence , An = πr02n4 = A1r4

An/A1 = n4

Taking log ,

ln(An/A1) = 4ln(n)

Hence Straight line with slope 4 .