The frequency of light emitted in the transition from the 167th orbit to the 160th orbit in hydrogen is 2.007 × 10^10 Hz.
The Rydberg formula can be used to calculate the frequency of light emitted when an electron in a hydrogen atom transitions from one energy level to another.
The Rydberg formula is a mathematical formula that describes the wavelengths of spectral lines in the hydrogen spectrum.
It was developed by the Swedish physicist Johannes Rydberg in 1888. The formula is particularly applicable to the spectral lines of hydrogen, but it can also be extended to other elements with modifications.
The formula is:
ν = R(1/n1^2 - 1/n2^2)
where:
ν is the frequency of light emitted (in Hz)
R is the Rydberg constant (1.097 × 10^7 m^-1)
n1 is the initial energy level
n2 is the final energy level
In this case, n1 = 167 and n2 = 160.
Plugging these values into the Rydberg formula, we get:
ν = 1.097 × 10^7 (1/167^2 - 1/160^2) = 2.007 × 10^10 Hz
Therefore, the frequency of light emitted in the transition from the 167th orbit to the 160th orbit in hydrogen is 2.007 × 10^10 Hz.