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The energy difference between the ground state of an atom and its excited state is 3 x 10-19 J. What is the wavelength of the photon required for this transition?
  • a)
    6.6 x 10-34 m
  • b)
    3 x 10-8 m
  • c)
    1.8 x 10-7 m
  • d)
    6.6 x 10-7 m
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
The energy difference between the ground state of an atom and its exci...
ΔE = hc/λ
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The energy difference between the ground state of an atom and its exci...
The energy difference between the ground state and the excited state of an atom can be calculated using the formula:

ΔE = E2 - E1

where ΔE is the energy difference, E2 is the energy of the excited state, and E1 is the energy of the ground state.

Given that ΔE = 3 x 10^-19 J, we can use this information to find the wavelength of the photon required for this transition.

1. Convert the energy difference to joules:
ΔE = 3 x 10^-19 J

2. Use the equation relating energy and wavelength of a photon:
ΔE = hc/λ

where h is Planck's constant (6.626 x 10^-34 J·s), c is the speed of light (3 x 10^8 m/s), and λ is the wavelength of the photon.

3. Rearrange the equation to solve for wavelength:
λ = hc/ΔE

4. Substitute the given values into the equation:
λ = (6.626 x 10^-34 J·s)(3 x 10^8 m/s)/(3 x 10^-19 J)

5. Simplify the equation:
λ = (6.626 x 10^-34 J·s)(3 x 10^8 m/s)/(3 x 10^-19 J)
= 6.626 x 10^-34 J·s · 3 x 10^8 m/s / 3 x 10^-19 J
= (6.626 x 3) x (10^-34 J·s x 10^8 m/s) / (3 x 10^-19 J)
= 19.878 x 10^-26 J·m / 10^-19 J
= 19.878 x 10^-7 m
= 1.9878 x 10^-6 m

Therefore, the wavelength of the photon required for this transition is approximately 1.9878 x 10^-6 m, which can be expressed as 1.9878 μm. The closest answer choice is option D, 6.6 x 10^-7 m, which is approximately 660 nm.
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