Verified answer

Answer:

Option 1

Explanation:

The energy corresponding to a spectral line can be calculated using the formula:

E = hν

where E is the energy, h is Planck's constant, and ν is the frequency of the spectral line.

The wave number (k) of the spectral line is related to its frequency (ν) as:

k = ν/c

where c is the speed of light.

Therefore, we can find the frequency of the spectral line as:

ν = kc

Given that k = 5 x 10^5 m^-1, and c = 3 x 10^8 m/s, we have:

ν = kc = (5 x 10^5 m^-1) × (3 x 10^8 m/s) = 1.5 x 10^14 Hz

Now, we can find the energy corresponding to this frequency as:

E = hν = (6.626 x 10^-34 J s) × (1.5 x 10^14 Hz) = 9.94 x 10^-20 J

The answer is not one of the given options, so we can round it off to 3 significant figures and express it in kJ:

E = 9.94 x 10^-20 J = 9.94 x 10^-23 kJ (rounded off to 3 significant figures)

Therefore, the energy corresponding to the given spectral line is 9.94 x 10^-23 kJ (option 1).