Question

Hydrogen has a red emission line at 656.3 nm, what is the energy and frequency of a photon of this light? Note: planck's constant = 6.626 x 10–34 j·s, speed of light = 2.998 x 108 m/

Answer 1

Answer:- Energy =
`3.03*10^-^1^9J` and frequency =
`4.57*10^1^4s^-^1` .

Solution:- The wavelength is given as 656.3 nm and it asks to calculate energy and frequency of a photon of this light. When the wavelength is given then the energy is calculated by using the equation:

`E=(hc)/(\lambda )`

where, E is energy, h is planck's constant, c is speed of light and
`\lambda` is the wavelength.

Wavelength is given in nm and for calculations of energy we need it in m.

`\lambda =656.3nm((10^-^9m)/(1nm))`

`\lambda =6.563*10^-^7m`

Let's plug in the values in the equation to calculate energy:

`E=(6.626*10^-^3^4J.s*2.998*10^8m.s^-^1)/(6.563*10^-^7m)`

E =
`3.03*10^-^1^9J`

Frequency is calculated for the given wavelength using the equation:

`\\u =(c)/(\lambda )`

let's plug in the values in the equation:

`\\u =(2.998*10^8m.s^-^1)/(6.563*10^-^7m)`

`\\u =4.57*10^1^4s^-^1`

So, the energy of the photon for given wavelength is
`3.03*10^-^1^9J` and the frequency is
`4.57*10^1^4s^-^1` .

Answer 2

We know that

Speed of light = wavelength X frequency

Energy of light = h X frequency

Where

h = planck's constant = 6.626 x 10–34 j·s

frequency = speed of light / wavelength = 2.998 x 10^8 m/s / 656.3 X 10^-9

frequency = 4.57 X 10^14 / s

Energy = 6.626 x 10–34 j·s X 4.57 X 10^14 / s = 3.028 X 10^-19 Joules