Energy Level Formula and Example Sums

Energy Level Formula :

Energy Level Formula  is radius of energy level r(n)(m) in meter is equal to the  square of n2 and multiply the product of radius r(1)(m) in meter. Hence the Energy level formula can be written a,

E(n)= – 1/n² * 13.6 eV

Other forms of energy level formula,

If n1 is the lower energy level and n2 is the higher energy level, the equation becomes

ΔE = hμ = -(1/n2² – 1/n1²) 13.6 eV

Taking negative signs inside,

ΔE = hμ = (1/n1² – 1/n2²) 13.6 eV

This form of energy level formula is used in case of transitions between two energy levels to find the energy of the emitted photon.

Sample Problems :

Example 1:

calculate the energy? In terms of electrons absorbing and emitting photons to shift energy levels, the hydrogen spectrum has the longest wavelength (nhigh) of 4 and the shortest wavelength (nlow) of 2. Using the Bohr energy level formula,

Solution :


nhigh = 4

nlow = 2

By using the Bohr formula energy levels we get,

ΔE = (1/n2low − 1/n2high)13.6eV

ΔE = (1/22 − 1/42)13.6eV

ΔE = (0.25 – 0.0625) *13.6eV

ΔE = 0.1875 * 13.6eV

ΔE = 2.55eV

Example 2:

Calculate the amount of energy that has been released? Electrons in one mole of hydrogen atoms fall from the n=3 energy level to the n=2 energy level.

Solution :

Using the following equation for the energy of an electron in Joules:

ΔE = −2.18 *10−18(1/n2f − 1/n2i)


1mol = 6.02 *  1023 molecules

Combining equations and plugging in values:

ΔE1mole = 6.02 * 1023 * −2.18 * 10−18(1/22−1/32)

ΔE1mole = −182kJ

182kJ would be released

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