Verify that the combined value of the constants appearing in Eq. 39-33 is 13.6eV

Short Answer

Expert verified

It is verify that the combined value of the constants appearing in Eq. 39-33 is 13.6 eV.

Step by step solution

01

The energy produce by electron

Energyof an atom in the nth level of the hydrogen atom is given by,

En=mee48ε02h2.1n2……. (1)

Where,Enis energy produce by electron, meis mass of electron, e is electric charge of electron, ε0is permittivity, h is plank’s constant and n is Quantum number.

02

Step 2: Verifying that the combined value of the constants appearing in Eq. 39-33 is 13.6 eV

From equation (1) we have,Energy of an atom in the nth level of the hydrogen atom is given by,

En=mee48ε02h2.1n2

Now, we have,me=9.11×10-31kg

e=1.6×10-18Cε0=8.85×10-12F/m2h=6.63×10-34J.s

Now, put all values in equation (1) we get,

En=(9.11×10-31kg)(1.6×10-18C)48(8.85×10-12F/m2)26.63×10-34J.s2.1n2=2.18×10-18n2

Now, we know thatrole="math" localid="1661838773953" 1eV=1.6×10-19J

By substituting 1eV=1.6×10-19Jin above equation, we get

En=2.18×10-18n2(1.6×10-19J/eV)J=-13.6eVn2

Now, in equation 39-33 we get, En=-13.61eVn2.

So, we can say thatthat the combined value of the constants appearing in Eq. 39-33 is 13.6 eV .

Hence it is verified.

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