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:

a solenoid is created by wrapping a l = 90 m long wire around a hollow tube of diameter d = 4.5 cm.   the wire diameter is d = 0.9 mm.   the solenoid wire is then connected to a power supply so that a current of i = 9 a flows through the wire.

randomized variablesl = 90 m

d = 4.5 cm

d = 0.9 mm

i = 9 a                                          

write an expression for the number of turns, n, in the solenoid. you do not need to take into account the diameter of the wire in this calculation.

calculate the number of turns, n, in the solenoid.

write an expression for the length of the solenoid (l2) in terms of the diameter of the hollow tube d.

calculate the length of the solenoid (l2)   in meters.

calculate the magnitude of the magnetic field at the center of the solenoid in teslas.

explanation: