the ground state energy of hydrogen atom is -13.6eV, if an electron make a transition from an energy level -0.85 eV, calculate the wavelength of the spectral line emitted. to which series of hudrogen spectrum does this wavelength belong?
Answers
Answer: 6
Explanation:
From the n
th
state, the electron may go to (n−1)
th
state, ...., 2nd state or 1st state. So there are (n 1) possible transitions starting from the n
th
state. The atoms reaching (n−1)
th
state may make (n 2) different transitions. The atoms reaching (n−2)
th
state may make (n 3) different transitions. Similarly for other lower states. During each transition a photon with energy hν and wavelength λ is emitted out. Hence, the total number of possible transitions is equal to the number of photons emitted. The total number of possible transitions is
(n−1),(n−2),(n−3),................,3,2,1=
2
n(n−1)
Therefore, for transition of an electron from higher energy state n = 4 to lower energy state n = 1 the number of photons emitted are
2
n(n−1)
=
2
4(4−1)
=
2
12
=6
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