Hydrogen atom is excited from ground state to another state with principal quantum number equal to 4. Then the number of spectral lines in the emission spectra will be :
Explanation
Hint: Energy of photons = E=hcλ
Solution:
Step 1: Find the energy of photon.
Given: hc=12500eV−A∘,λ=980A∘
Energy of photons = E=hcλ
⇒E=12500980=12.75eV
Step 2: Find the excited state
Now, Energy of hydrogen atom in nth shell =En=−13.6n2
Energy absorbed by hydrogen atom = energy of photons
⇒En−E1=E
⇒−13.6n2−[−13.612]=12.75eV
⇒13.6−13.6n2=12.75
⇒1−1n2=12.7513.6
⇒1−1n2=0.9375
⇒1n2=1−0.9375=0.0625
Step 3: Find radius in the excited state.
Radius of hydrogen atom = r=n2a0
⇒r=(4)2a0
⇒r=16a0
So, Radius of hydrogen atom in excited state is 16a0
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