The minimum energy of a photon that can produce one hydrogen atom from water is
The frequency of the photon is .
The wavelength of the photon is .
Further Explanation:
Frequency is defined as number of times n event occurs in unit time. It is generally applied to waves including light, sound, and radio waves. It is denoted by and its SI unit is Hertz (Hz).
Wavelength is the characteristic property of a wave. It is defined as the distance between two successive crests or troughs. A crest is that point where there is maximum displacement of the medium whereas trough is a point that has minimum displacement of the medium. It is represented by and its SI unit is meter (m).
First, the energy required to produce one hydrogen atom in joule can be calculated as follows:
     …… (1)
Here, is an Avogadro's number and has a value .
Substitute for and for in equation (1).
Thus the energy of a photon that can free one atom of hydrogen is .
The expression of frequency and energy is as follows:
       …… (2)
Here, is a frequency of photon and h is a Plank’s constant and has a value .
Rearrange equation (2) to calculate the frequency of the photon as follows:
       …… (3)
Substitute for h and for E in equation (3).
Thus the frequency of photon is .
The expression to calculate the wavelength from energy of the photon is as follows:
         …… (4)
Here is a wavelength of a photon and c is a speed of light.
Rearrange equation (4) to calculate wavelength of the photon as follows:
                …… (5)
Substitute for h, for c and for E in equation (5).
Hence wavelength of the photon is equal to .
Learn more:
1. Ranking of photons according to the wavelength of transition:
2. Calculate de Broglie wavelength of golf ball:
Answer details:
Grade: Senior School
Subject: Chemistry
Chapter: Structure of atom
Keywords: Hydrogen atom, cheapest source of h2, 467 kj, 1 mol of h atom, frequency wavelength.