Question

An excited H-like species when bombarded by photons of wavelength 54 nm gets excited to
another excited state. In returing back to ground slate it emits, a total six different types of
photons. Out of six different photons three have wave length less than 54 nm. Determine atomic
no. of H-like species (Shorest wavelength of Lyman series of H-atom is 90 nm.)​

Answer 1

Concept:

The Rydberg concept is a mathematical method for calculating light wavelength. The energy of an electron varies when it moves from one atomic orbit to another.

Given:

H like species

Bombarded by photons of wavelength 54 nm

Emit 6 different type of photons while returning back

3 photon wavelength > 54nm

3 photon wavelength < 54nm

Find:

Atomic number of that species

Solution:

First calculate the Wavelengths of the photons using

1/λ = ( 1/λ₁ + 1/λ₂ + 1/λ₃ ) + ( 1/λ₄ + 1/λ₅ + 1/λ₆ )

For the first three its given wavelength < 54 nm, so the next three wavelength should be > 54 nm

Because the first three are supplied at <54 nm, the next three should be >54 nm.

However, this is not the precise figure. You should provide additional information to determine the photon λ values.

Second, E should be determined from the λ value set.ΔE = hc/λ

Next, compute the n1 and n2 values.

ΔE = Rhc z² ( (1/n₁²) - (1/n₂²) )

Next ionisation energy = - E

E value or value of the λ of new species should be provided when computing atomic number.

Hence, the value of E or λ of new species should be given to us to calculate the final result.

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