Photoelectric Effect and Related Concepts

Which of the following wavelengths (in nm) of electromagnetic radiation will produce photoelectrons of the least kinetic energy if the radiation is incident on a material with a work function of 4.80 $\mathrm{e}\mathrm{V}$?

(A) 992
(B) 496
(C) 248
(D) 124
(E) 62

A stationary atom of mass $4.00\times 10^{-26}kg$ spontaneously emits a photon of energy 10.0 $eV$. Which one of the following choices best represents the speed, in units of $m/s$, of the atom after emitting the photon?

(A) $4.00\times 10^{7}$ (B) 8. $94\times 10^{3}$ (C) $1.33\times 10^{-1}$ (D) $1.58\times 10^{-4}$ (E) 2. $50\times 10^{-8}$

There is a quantity called the Planck time, $t_{Planck}$, which is computed in terms of constants as $\displaystyle t_{Planck}^{2}=\frac{\mathrm{h}G}{c^{n}}$ where $\mathrm{h}$ is Planck's constant divided by $2\pi, G$ is the Universal Gravitational Constant, and $c$ is the speed of light. In order for this expression for time to be consistent, what is the numerical value of $n$, the power to which the speed of light is raised?

(A) 2
(B) 3
(C) 4
(D) 5
(E) 6

Planck's constant is multiplied by the speed of light. The resulting value then is divided by three meters. This final value has the units of which one of the following quantities?

(A) Force
(B) Linear Momentum
(C) Speed
(D) Frequency
(E) Energy

Light of wavelength 250 $nm$ shines onto a metallic surface. It is known that the electrons ejected from the surface range in speed as $0\displaystyle \leq v\leq 4.85\times 10^{5}\frac{m}{s}$. What is the work function of the surface?

(A) 4.97 $eV$
(B) 1.60 $eV$
(C) 3.63 $eV$
(D) 4.30 $eV$
(E) 1.34 $eV$

An $\mathrm{x}$-ray photon collides with a free electron, and the photon is scattered. During the collision:

(A) there is conservation of momentum but not energy

(B) there is conservation of neither momentum nor energy

(C) there is conservation of energy but not momentum

(D) there is conservation of both momentum and energy

(E) impossible to predict if momentum and energy are conserved without additional information

Which of the following wavelengths (in nm) of electromagnetic radiation will produce photoelectrons of the least kinetic energy if the radiation is incident on a material with a work function of4.80 $\mathrm{e}\mathrm{V}$?

(A) 992
(B) 496
(C) 248
(D) 124
(E) 62

Which of the following scientists is credited with first introducing the concept that energy is quantized, laying the foundation for quantum mechanics?
(A) Niels Bohr
(B) Erwin Schrödinger
(C) Max Planck
(D) Albert Einstein
(E) Louis de Broglie

An electromagnetic wave has a magnetic field given by the expression (in Cartesian coordinates) $\vec{B}(x, y, z, t)=\left(6.0 \times 10^{-6}\right) \cos \left(2.21 \times 10^{7} z-6.63 \times 10^{15} t\right) \widehat{x}$. At time $t=0$ and position $x=y=z=0$, what is the direction of the electric field associated with this wave?
(A) +x
(B) -x
(C) +y
(D) -y
(E) +z

The following expressions are non-mks units in physics. Identify the physical quantity that can be measured with the following units: (1) GeV, (2) GeV/c, (3) GeV/c²
(A) (1) Charge, (2) Velocity, (3) Mass
(B) (1) Energy, (2) Linear Momentum, (3) Mass
(C) (1) Mass, (2) Angular Momentum, (3) Torque
(D) (1) Energy, (2) Angular Momentum, (3) Charge
(E) (1) Energy, (2) Linear Momentum, (3) Torque

Which of the following statement(s) can be associated with Bohr's theory of the atom?
I. An electron orbiting the nucleus can change its energy continuously.
II. An electron orbiting the nucleus emits energy and falls into the nucleus.
III. An electron orbits the nucleus without radiating energy and can change its energy only by a specific, quantized amount, when it moves between the orbits.
IV. Electrons can only orbit the nucleus in specific circular orbits with fixed angular momentum and energy.
(A) I and II
(B) II and IV
(C) II and III
(D) III and IV
(E) I, II, III and IV