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A photon with a wavelength of 397nm is emitted from an electron in energy level 7 of a Hydrogen atom. What is the new energy level of the el
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Answer:
New energy level is n = 2
Explanation:
ΔE = energy released by e⁻ transition n = 7 to n(final) = – h·c/λ
h = Planck’s Constant = 6.63 x 10⁻³⁴ j·s
c = speed of light in vacuum = 3 x 10⁸ m/s
λ = wavelength = 397 nm = 3.97 x 10⁻⁷ m
ΔE = – (6.63 x 10⁻³⁴j·s )(3 x 10⁸ m/s)/(3.97 x 10⁻⁷ m) = – 5.01 x 10⁻¹⁹ joule
Note: this is the transitional energy ‘released’ by the electron moving from n = 7 energy level to n(final) energy level. As released energy, the system should be represented by an exothermic process hence, the negative value for ΔE = – h·c/λ. The equivalent amount of energy is an absorption of electromagnetic energy (EMR) to promote the electron from n(final) to n = 7 and this would be endothermic as noted with a +h·c/λ .
The Bohr Model of the electron behavior postulates electron transitions by the release of a ‘discrete’ amount of EMR as emission spectra defined by the expression …
ΔE = E(final) – E(initial) => E(final) = ΔE + E(initial)
E(n) = positional (potential) energy content of electron while in energy level n and is defined by the expression E(n) = -R(H)/n²
R(H) = Rydberg Constant = 2.18 x 10⁻¹⁸ joules
n = positional energy level (in this case) = 7
E₇ = -2.18 x 10⁻¹⁸ j / (7)² = -4.45 x 10⁻²⁰ j (potential energy of n = 7 electron)
E(final) = ΔE + E₇ = (-5.01 x 10⁻¹⁹ j) + (-4.45 x 10⁻²⁰ j) = -4.455 x 10⁻¹⁹ j
E(final) = -R(H)/n²
=> n = SqrRt[R(H)/E(final)] = SqrRt[(-2.18 x 10⁻¹⁸ j)/(-4.455 x 10⁻¹⁹)] ≅ 2
New energy level is n = 2