Question

6.)How much energy is required to excite a hydrogen atom's electron from n=2 to n=5?

Enter your answer with 2 significant figures.

Note: Your answer is assumed to be reduced to the highest power possible.

6 b.) Calculate the wavelength of light that is required to excite a hydrogen atom's electron from n=2 to n=5?

Enter your answer in meters with 2 significant figures.

Note: Your answer is assumed to be reduced to the highest power possible.

Answer 1

Ans. #6. The amount of energy required to excite an electron in H-atom is given by-

E = R [(1/ n_i²) – (1/ n_f²)]                - equation 1

Where, R = Rydberg constant = 2.179 x 10^-18 J

n_i = initial energy state orbital

n_f = Final energy state orbital

Putting the values in above equation-

E = 2.179 x 10^-18 J [1/ (2²) – 1/(5²)] = 2.179 x 10^-18 J (0.21)

Or, E = 4.58 x 10^-19 J

Thus, required energy = 4.6 x 10^-19 J

#B. Part I: Energy of the photon is given by-

E = hv                        - equation 2

; where, h = Plank’s constant = 6.626 x 10-34 Js ;

v = frequency of photon

Or, 4.58 x 10^-19 J = 6.626 x 10^-34 Js x v

Or, v = (4.58 x 10^-19 J) / (6.626 x 10^-34 Js)

Hence, v = 6.912 x 10¹⁴ s^-1

Therefore, the required frequency of light, v = 6.912 x 10¹⁴ s^-1

Part II: For an EMR or photon,     c = v l                         - equation 3

Where, c = speed of light = 299792458 m/s

v = frequency

l = wavelength

Putting the values in equation 3-

299792458 m/s = (6.912 x 10¹⁴ s^-1) x l

Or, l = (299792458 m/s) / (6.912 x 10¹⁴ s^-1)

Hence, l =4.337 x 10^-7 m

Therefore, the required wavelength of light = 4.3 x 10^‑7 m