
Some energy levels of a molecule are shown in fig. The ratio of the wavelengths is given by:

Answer
146.7k+ views
Hint: we have been given two wavelengths and here are the two transitions. So assuming the corresponding two these two transitions, there is the emission of photons in each case. So firstly we will find the energy of that particular photon then using the relation which we have given in the formula, we will find the ratio between these two wavelengths.
Formula used
The energy of photons,
Here,
, will be the energy
, will be the planck's constant
, will be the speed of light
, will be the wavelength
Complete Step By Step Solution: As we know the formula for the energy of the photon and it can be written as
And from here, can be written as
And hence we can say that
Now from the figure,
The energy of a photon of wavelength will be equal to
On solving the above equation, we get
Now we will calculate the Energy of the photon of wavelength and it will equal to
On solving the above equation, we get
So now we will calculate the ratios between the two energies
Therefore, it can be written as
Now on substituting the values, we get
So we will solve the final above equation to get the required ratios
Therefore, the option will be the correct choice.
Note: According to Einstein's equation anything that possesses energy has mass and anything that has mass has energy which is equal to the mass of the particle times square of the speed of light. Photons have rest mass but they have Energy which is equal to Planck constant times its frequency. So, if the photon has a fixed amount of energy which will be more than zero with zero rest mass but the photon does not exist which has moving mass so its energy will be zero.
Formula used
The energy of photons,
Here,
Complete Step By Step Solution: As we know the formula for the energy of the photon and it can be written as
And from here,
And hence we can say that
Now from the figure,
The energy of a photon of wavelength
On solving the above equation, we get
Now we will calculate the Energy of the photon of wavelength
On solving the above equation, we get
So now we will calculate the ratios between the two energies
Therefore, it can be written as
Now on substituting the values, we get
So we will solve the final above equation to get the required ratios
Therefore, the option
Note: According to Einstein's equation
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