For certain atom, there are energy levels A, B, C corresponding to energy values EA < EB < EC...

Q: For certain atom, there are energy levels A, B, C corresponding to energy values EA < EB < EC. Choose the correct option if λ1 , λ2, λ3 are the wavelength of radiations corresponding to the transition from C to B, B to A and C to A respectively:

(a) λ3 = λ1 + λ2

(b) \displaystyle \lambda_3 = \frac{\lambda_1 \lambda_2}{\lambda_1 + \lambda_2}

(c) λ1 + λ2 + λ3 = 0

(d) 3 λ2 = λ3 + 2 λ2

Ans: (b)

Sol:

\displaystyle \Delta E = h \nu = \frac{h c}{\lambda}

\displaystyle E_C - E_A  = ( E_C - E_B ) + ( E_B - E_A )

\displaystyle \frac{hc}{\lambda_3} = \frac{hc}{\lambda_1} + \frac{hc}{\lambda_2}

\displaystyle \frac{1}{\lambda_3} = \frac{1}{\lambda_1} + \frac{1}{\lambda_2}

\displaystyle \lambda_3 = \frac{\lambda_1 \lambda_2}{\lambda_1 + \lambda_2}

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