Question

The electron energy in hydrogen atom in its third
orbit is -1.51 eV. The energy emitted by the
electron to make transition to the second orbit
a. 0.51 eV
b. 0.76 eV
c. 0.84 eV
d. 1.89 eV​

Answer 1

Final Answer:

The energy emitted by the electron in hydrogen atom in its third orbit  to make transition to the second orbit is 1.89 eV, corresponding to the correct option d.

Given:

The electron energy in hydrogen atom in its third orbit is -1.51 eV.

Options for the energy emitted by the electron in hydrogen atom in its third orbit  to make transition to the second orbit are the following.

a. 0.51 eV

b. 0.76 eV

c. 0.84 eV

d. 1.89 eV​

To Find:

The energy emitted by the electron in hydrogen atom in its third orbit  to make transition to the second orbit is to be calculated.

Explanation:

The concept of energy of an electron that is important to arrive at the solution.

The energy of an electron in the nth energy level or the nth orbit of an atom is

$= -13.6\times \frac{Z^2}{n^2}$ eV.

The atomic number (Z) of the hydrogen atom is $Z=1$

Step 1 of 3

As per the given problem, the energy of an electron in the 3rd orbit in hydrogen atom is

$= -13.6\times \frac{1^2}{3^2}\\=-1.51\;eV$

Step 2 of 3

Using the information in the given problem, the energy of an electron in the 2nd orbit in hydrogen atom is

$= -13.6\times \frac{1^2}{2^2}\\=-3.40\;eV$

Step 3 of 3

In continuation with the above calculations, the energy emitted by the

electron to make transition to the second orbit from the third orbit is

$=-1.51-(-3.40)\\=-1.51+3.40\\=1.89\;eV$

Therefore, the required correct option is d as the required energy is 1.89 eV.

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