Question

A spectral line is emitted when an atom undergoes transition between two levels with a difference in energy of 2.4eV. What is the wavelength of the line?
287nm
507angstrome units
377angstrome units
518nm

Answer 1

Answer on Question 59096, Physics, Atomic and Nuclear Physics

Question:

A spectral line is emitted when an atom undergoes transition between two levels with a difference in energy of $2.4\,eV$. What is the wavelength of the line?

a) $287\,nm$

b) $507\,\text{\AA}$

c) $377\,\text{\AA}$

d) $518\,nm$

Solution:

We can find the wavelength of the line from the inverse relationship between the energy of the photon and the wavelength of the light given by the equation:

$$\Delta E = E_1 - E_2 = \frac{hc}{\lambda},$$

here, $\Delta E$ is the difference in energy when an atom undergoes transition between two levels, $h = 4.135 \cdot 10^{-15}\,eV \cdot s$ is the Planck's constant, $c$ is the speed of light, $\lambda$ is the wavelength of the spectral line we are searching for.

Therefore, from this equation we can calculate the wavelength of the line:

$$\lambda = \frac{hc}{\Delta E} = \frac{4.135 \cdot 10^{-15}\,eV \cdot s \cdot 3 \cdot 10^8\, \frac{m}{s}}{2.4\,eV} = 517 \cdot 10^{-9}\,m \approx 518\,nm.$$

Answer:

d) $518\,nm$

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