### Excited states of noninteracting Fermion and Bose systems

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A one-dimensional quantum well of width 19 nm is created, and measurements show that the energy difference between the ground state and the first excited state is 0.19 eV. What is the eﬀective mass of the electron in the well? Answer in units of kg.

Part a Consider an electron in an infinite well of width 0.03 nm. Given : 1eV = 1.60218 × 10^-19 J hbar = 1.05457 × 10^-34 J s , What is the ground-state energy of the electron, in electron volts? Answer in units of keV. Part b What is the energy of the first excited state? Answer in units of keV.

The problem reads as: "The magnetic field permeating a region of space represents stored energy. This energy is often quantified in terms of its density (magnetic energy per unit volume) given by B^2/(2*u) where u=4*pi X 10^(-7). Suppose an "X2" flare occurs within a volume of 10^12 km3 over a sunspot pair initially permeate

1. A thin, spherical, conducting shell of radius R is mounted on an insulating support and charged to a potential of -125V. An electron is then fired directly toward the center of the shell, from point P at distance r from the center of the shell ( r>>R). What initial speed Vo is needed for the electron to just re

Protons exit a high speed proton machine at a speed of 1.50 * 10^6 m/s. A device needs to stop the protons safely. Protons will embed themselves in a metal target, but protons traveling faster than 1.30 * 10^5 m/s emit dangerous x rays when they hit. The protons must be slowed down to an acceptable speed, then let them hit a

A parallel plate capacitor with plate separation d is connected to a battery. The capacitor is fully charged to Q Coulombs and a voltage of V. (C is the capacitance and U is the stored energy.) Answer the following questions regarding the capacitor charged by a battery. For each statement below, select True or False. 1. Aft

A particle of mass 3.5 MeV/c2 and kinetic energy 4.5 MeV collides with a stationary particle of mass 0.5 MeV/c2 . After the collision, the particles stick together. (part 1 of 5) Find the total energy of the first particle before the collision. Answer in units of MeV. (part 2 of 5) Find the speed of the first particl

For simple harmonic oscillator H = p^2/(2m) + (K/2)x^2 turn on the potential V(x) = cx^4 Calculate the first order correction to the ground state energy. Prove that the first order energy correction vanishes for all n = odd integer excited state levels.

A.) The filament of a light bulb has a temperature of 3.1 103 °C and radiates 70 watts of power. The emissivity of the filament is 0.38. Find the surface area of the filament. B.) A car parked in the sun absorbs energy at a rate of 550 watts per square meter of surface area. The car reaches a temperature at which it radiat

A dish of lasagna is being heated in a microwave oven. The effective area of the lasagna that is exposed to the microwaves is 1.6 10-2 m2. The mass of the lasagna is 0.26 kg, and its specific heat capacity is 3400 J/(kg°C). The temperature rises by 80.0°C in 7.0 minutes. What is the intensity of the microwaves in the oven?

A wooden rod of negligible mass and length 80.0 cm is pivoted about a horizontal axis through its center. A white rat with mass 0.550 kg clings to one end of the stick, and a mouse with mass 0.170 kg clings to the other end. The system is released from rest with the rod horizontal. If the animals can manage to hold on, what a

For this question you need to know that an electron accelerated through an electric potential difference of V volts acquires a kinetic energy of V eV. (This question is best done by not converting to joules, but by exploiting the fact that mec2 is given as 0.511 MeV). i) What is v/c for an electron? a) Striking the screen

A .15kg block of ice is placed on a horizontal table. It is pushed back compressing a spring .045m, and the spring's constant is 1900N/m. The spring's mass is negligible. The tabletop is 1.2m above the floor. When the spring is released, the block slides off the table and onto the floor. With negligible friction between the

A capacitor has a charge of 30 uC (fancy u). The potential difference between the conductors is 400 is V. What is the capacitance?

Three point charges are on the x axis: q1 at the origin, q2 at x=3 m, and q3 at x= 6 m. Find the electrostatic potential energy for (a) q1=q2=q3=2uC (u is the fancy u sign); (b) q1=q2=2uC, and q3 -2uC; and (c) q1=q3 = 2uC, and q2= -2uC.

Two point charges of values +3.4 and +6.6 micro-coulombs, respectively, are separated by 0.20 m. What is the potential energy of this 2-charge system? (ke=9.00 x 10^9 Nm^2/C^2) EPE=kq1q2/r

The Cosmotron, which began operation in the early 1950's at Brookhaven National Laboratory, accelerated protons to kinetic energy of 3000 MeV. Find the total energy, pc, βo, and γo for these protons.

See attached file for full problem description. Previously it was considered a force of the form f = ixy + jcx^2 + kz^3, and found a value of "c" from the following list such that this was a conservative force. Note: there must really be extra 'constants' in front of each term, with magnitude 1 but the proper units (such as

The electric potential energy stored in the capacitor of a defibrillator is 73 J, and the capacitance is 120 microFarads. What is the potential difference across the capacitor plates?

A conducting sphere of radius R carries a charge Q. a) Calculate stored energy b) Calculate the radius R(sub 0.5) within which the field energy is one half the total stored energy. c) Calculate the radius R(sub0.9)

A block of mass m slides without friction on a table with speed v. It hits and compresses a spring of force constant k by a distance l. The spring then expands again ejecting the block in the opposite direction as it was originally traveling. Neglecting the mass of the spring, what is the speed of the object after it is ejected

1. A candle flame can be seen at night at a distance of 2 km by the unaided eye. If it emits visible light at the rate of 0.02 J/s, what is the number of photons that enter the eye per second? 2. What is the wavelength of a beam of ultraviolet light if its photon energy is 10 eV? If the beam produces photoelectrons from iron,

A block of mass m: I.62 kg slides down a frictionless incline (attached). The block is released a height h : 3.91m above the bottom of the loop. See attached for full problem description.

This exercise is for a Bose-Einstein condensate of indistinguishable atoms which do not interact with each other and are in a 3-dimensional harmonic well. The system is described by the following Hamiltonian (see attached file).

By simultaneously conserving energy and momentum, calculate the energy of the neutron emitted in the forward direction by a beam of 150 keV deuterons undergoing the D-T (deuterium-tritium) reaction in a tritium target.

The average sound intensity inside a busy restaurant is 3.2 x 10^-5 W/m^2. How much energy goes into each ear (area=2.1 x 10^-3 W/m^2) during a one hour meal?

A stone of mass 0.62kg is fired upwards at an angle to the ground and with a speed of 5.5 m s-1, as shown in the figure in the attachment. The figure shows the path of the stone until it strikes the ground at point C. Disregard air resistance. Take the acceleration, g, due to gravity to have a value of 9.8 m s-2. Calculate

A perfectly insulated container contains 70 g of water and has a small heater immersed in water. The temperature of the water is 40 degrees Celsius, and the heater is connected to a 12V battery via a switch. When the heater is switched on, an electric current of 13A flows through its heating element and the temperature of the w