TG EAMCET 3 May 2025 Shift 2 Paper

Step 1: Find the Total Energy (TE) from the Given Potential Energy (PE)
The potential energy of the electron is given as -6.8 eV .
We use the relation: PE=2(TE)
This means: TE=‌

PE

2

=‌

−6.8

2

=−3.4eV
Step 2: Find the Value of n (Principal Quantum Number)
For a hydrogen atom, the total energy formula is: TE=‌

−13.6

n2

Set this equal to the TE we found: −3.4=‌

−13.6

n2

Solve for n2:n2=4
So, n=2
Step 3: The Electron is in the Second Orbit
Since n=2, the electron is in the second Bohr orbit.
Step 4: Use Bohr's Model and de-Broglie Hypothesis
According to Bohr and de-Broglie:
2πrn=nλ
This gives: λ=‌

2πrn

n

Step 5: Use the Formula for the Radius of Orbit

Radius of the nth orbit: rn=n2r0
For n=2 (second orbit): r2=22r0=4r0
Step 6: Calculate the de-Broglie Wavelength
Plug r2 into the earlier formula:
λ=‌

2πr2

2

=‌

2π

2

×4r0=4πr0