Question

One of the electron transitions in a hydrogen atom produces infrared light with a wavelength of 7.464 x 10⁻⁷m. What amount of energy causes this transition? Calculate the wavelength, in meters, associated with this radiation.

A) 6.63 x 10⁻³⁴J
B) 1.60 x 100⁻¹⁹J
C) 8.44 x 10⁻⁷m
D) 1.34 x 10⁻⁶m

Answer 1

The energy causing the transition is approximately 2.88 x 10^-19 J.

Step-by-step explanation:

The energy associated with an electron transition in a hydrogen atom can be calculated using the equation:

E = ƜƓ

where E represents the energy, Ɯ is the Planck's constant (6.63 x 10-34 J·s), and Ɠ is the frequency. To calculate the energy causing the transition, we need to find the frequency of the infrared light with a wavelength of 7.464 x 10-7 m. The equation relating wavelength, frequency, and the speed of light (c) is:

c = Ɠλ

where c is approximately 3 x 108 m/s. Rearranging the equation, we can solve for the frequency:

Ɠ = c/λ

Substituting the given wavelength, we have:

Ɠ = (3 x 108 m/s) / (7.464 x 10-7 m)

Ɠ ≈ 4.017 x 1014 Hz

Now we can substitute the frequency into the energy equation:

E = (6.63 x 10-34 J·s) (4.017 x 1014 Hz)

E ≈ 2.88 x 10-19 J