What is the change in energy ΔE of the hydrogen atom as the electron makes the transition from the n=3 energy level to the n=1 energy level?Express your answer numerically in electron volts.

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:

russian is not my first language, so i'm afraid i can't write out an answer in russian, but hopefully you can find a way to do so. here's my best translation of the problem: you're given a plot of a particle's position in one-dimensional space over time, and you're asked to find either the total distance traveled by the particle after 6 seconds had elapsed, or the total displacement of the particle after 6 seconds.

if you want the total distance traveled, you would first need to determine the particle's velocity as a function of time, then integrate that over the 6-second interval. we know the position function is quadratic with roots at 0 and 6, so we have

where is unknown. because the position is parabolic, there is symmetry about the midpoint at , and we know that

so that the position function is

which means the velocity is

then the total distance traveled is

so the total distance traveled is 20 m.

on the other hand, if you want to find displacement: the particle starts at and ends at , so its displacement is 0.

the right answer is 0.3 meters per second