The skier, who weighs 700 N, slipped into a 25 m high mountain. Calculate the skier’s potential energy at the top of the mountain.
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Ответ:
An
Z is the atomic number , i.e. the number of protons in the nucleus, and RE is the Rydberg energy.
RE = mₑ ∙e⁴ / (2∙ħ²) ≈ 13.6 eV
(mₑ mass of electron, e electron charge, ħ reduced Planck constant)
A)
Atomic number of hydrogen is Z = 1, so
E = - RE/n²
The change in energy of the hydrogen atom si the difference between the initial and final energy of the electron:
ΔE = E₁ - E₃ = - RE/1² - (-RE/3²) = RE∙((1/9 - 1) = -12.1 eV
That means the energy of the atom reduces by 12.1 eV
B)
The energy of the emitted photon equals the energy loss of the atom:
Ep = - ΔE = 12.1 eV
Energy Ep and wavelength λ of a photon are related as [2]:
Ep = h∙c / λ
whee h is Planck constant and c speed of light
Hence
λ = h∙c / Ep
= 4.136×10⁻¹⁵ eV∙s 2.998×10⁸ m/s / 12.1 eV
= 1.026×10⁻⁷ m/s
= 102.6 nm
C)
Helium has atomic number Z = 2, so the energy of an electron at level in He⁺ is:
E = - RE ∙ 2²/n² = - 4∙RE/n²
The energy required to lift the electron from level 2 to some higher level n is:
ΔE = E_n - E₂ = - (4∙RE/n²) - (- 4∙RE/2²) = RE∙(1 - (4/n²))
This energy difference equals the energy of the photon:
Ep = RE∙(1 - (4/n²))
<=>
(4/n²) = 1 - (Ep/RE)
=>
n² = ( 4 / (1 - (Ep/RE)) )
=>
n = √( 4 / (1 - (Ep/RE)) )
= √( 4 / (1 - (12.01eV/13..6eV)) )
= 6swer:
Explanation: