Question

Motivating experiments

Show all work to earn full credit for computational problems.
(a) In a photoelectric effect experiment, light with wavelength 250.0 nm is incident on a metal surface, and photoelectrons with wavelength 1.10 nm are produced. Calculate the work function of the metal and give your answer in eV.
(b) State whether the following physical quantities are discrete or continuous variables in the Rayleigh-Jeans and Planck models of blackbody radiation (i.e. write two words for each part). The meaning of "discrete" is "only certain values are allowed".
(i) The frequencies of the oscillators in the cavity.
(ii) The amount of energy contained in an individual oscillator.
(iii) The temperature.
(c) In a blackbody radiation experiment, the peak wavelength from the radi- ating object is given as 850.0 nm. Calculate the total power per unit surface area emitted from the object, and give your answer in SI units.
(d) In Bohr's model of the hydrogen atom and one-electron ions, the electron is modeled as a classical particle in a circular orbit. Name the lightest one- electron ion (lowest Z) where the classical velocity of the electron in the n = 1 orbit exceeds the speed of light.

Answer 1

a) Φ = 4.97 eV, b) the Planck model, it assumes that the frequencies are discrete and therefore it raises a discrete expression for the energi

E = h f

c) p / A = 7.66 10⁶ W / m²

Step-by-step explanation:

a) the photoelectric effect was described by Einstein, assuming the existence of light quanta, which is why it is described by the equation

h f = K + Ф

in this case the speed of light is

c = λ f

h c / λ = K + Φ

if we assume that the scientific energy of the electrocutors is zero

hc / λ = fi

Φ = 6.63 10⁻³⁴ 3 10⁸/250 10⁻⁹

Φ = 7,956 10⁻¹⁹ J

reduced to eV

Φ = 7,956 10⁻¹⁹ (1 ev / 1.6 10⁻¹⁹ J)

Φ = 4.97 eV

b) in the Rayleigh-Jean model the quantities are all continuous, but does not explain phenomenon at high energy

In the Planck model, it assumes that the frequencies are discrete and therefore it raises a discrete expression for the energi

E = h f

temperature is a continuous variable in both models

c) the power emitted by a black body is given

P = σ A e T⁴

for a black body, emicivity is one

P / A = σ T⁴

let's use Wien's law of displacement to find the temperature

λ T = 2,898 10⁻³

T = 2,898 10⁻³ / λ

T = 2,898 10⁻³ / 850 10⁻⁹

T = 3,409 10³ K

we calculate

P / A = 5,670 10⁻⁸ 3409⁴

p / A = 7.66 10⁶ W / m²

d) The Bohr model is slightly modified to include the atoms with an electron

En = - k e2 / 2 ao (Z2 / n2)

r = n2 ao / Z