Question

For the hydrogen atom, the transition from the 2p state to the is state is accompanied by the emission of a photon with an energy of 16.2x10-19 J. For a Cl atom, the same transition (2p to 1s) is accompanied by the emission of x-rays of wavelength 4.73 A. What is the energy difference between these states in chlorine? The energy difference between these states in chlorine is the corresponding energy difference for hydrogen. The energy difference between these states in chromium would be expected to be the corresponding energy difference for chlorine. Submit Answer 5 question attempts remaining

Answer 1

Answer -

Given,

Transition levels

n final = 1s

n initial = 2p

Energy for the transition of H from 2p to 1s = 16.2 * 10^-19 J

wavelength in Case of Cl in these states = 4.73 A

Energy Difference for Chlorine from 2p to 1s = ?

We know that,

E = hc/$\lambda$

where, E = Energy

h = planks constant (6.62607015×10⁻³⁴ Js)

c = Speed of light (3 * 10⁸ m/s)

$\lambda$ = wavelength

Also, 1A = 10^-10 m

So, 4.73 A = 4.73 * 10^-10 m

Put values in formula,

E = (6.62607015×10⁻³⁴ Js * 3 * 10⁸ m/s) /4.73 * 10^-10 m

Energy difference between these states of Cl = 42.02 * 10^-17 J [ANSWER]

Energy Difference of H atom = 0.162 * 10^-17 J

Energy Difference of Cl atom = 42.02 * 10^-17 J

Difference in energy differences of Cl and H = (42.02 - 0.162) * 10^-17 J = 41.858* 10^-17 J

So,The energy differences between these state in chlorine is Greater (Greater by 41.858* 10^-17 J) than the corresponding energy difference hydrogen [ANSWER]

Now,

According to Rydberg's Equation,

1/$\lambda$ = RZ² {[1/(n_f)²] - [1/(n_i)²]}

where $\lambda$ = wavelength in m

R = 1.097x 10⁷ m^-1

Z = atomic Number

nf and ni are energy levels

For, Chromium

1/$\lambda$ = 1.097x 10⁷ m^-1 * (24²) {[1/(1)²] - [1/(2)²]}

$\lambda$ = 2.11 * 10^-10 m

Also, E = hc/$\lambda$

where, E = Energy

h = planks constant (6.62607015×10⁻³⁴ Js)

c = Speed of light (3 * 10⁸ m/s)

$\lambda$ = wavelength

Put values in formula,

E = (6.62607015×10⁻³⁴ Js * 3 * 10⁸ m/s) / 2.11 * 10^-10 m

Energy difference between these states of Chromium = 9.459 * 10^-16 J

Energy Difference of Cr atom = 94.59 * 10^-17 J

Energy Difference of Cl atom = 42.02 * 10^-17 J

Difference in energy differences of Cr and Cl = (94.59 - 42.02) * 10^-17 J = 52.57* 10^-17 J

So,The energy differences between these state in chromium is Greater (Greater by 52.57* 10^-17 J) than the corresponding energy difference hydrogen [ANSWER]