Quantum Mechanics Answers

Show that the quantisation condition (2.4.39) of the orbital angular momentum in the Bohr model is equivalent to imposing that the circumference of a circular orbit is an integer multiple of the de Broglie wavelength.

Calculate the de-Broglie wavelength of a proton whose kinetic energy is equal to the rest mass energy of an electron (mass of proton is 1836 times that of electron). 

What is the ratio of the relativistic mass to the rest mass for an electron and a proton when it is accelerated from rest through a potential difference of 15mv(mega volts)

take mass of electron=0.5mEv and mass of proton=1000mEv

Show that the orbit nearest to the nucleus in the hydrogen atom accommodates one electron waves. Given that the energy of the electron in the orbit is 13.6 eV, h=6.625x10-34Js, m=9.11x10-31kg, Bohr radius r1 =5.292x10-11 m.

Find the lowest energy of an electron confined in a cubical box of each side 1 Å?

A stream of electrons, each of energy 𝑬 = 𝟑𝒆𝑽 is incident on a potential of height 𝑽𝟎 = 𝟒𝒆𝑽 . The width of the barrier is 20Å. Calculate the percentage transmission of the beam through this barrier.?

At what fraction of the speed of light does a particle travel if it's kinetic energy is twice it's rest mass

Show that quantum mechanics reduces to classical mechanics for 𝒉 →0

 A hydrogen balloon at the Earths surface has a volume of on a day when the temperature is and the pressure 1 atm. What is the mass of hydrogen? The balloon rises and expands as the pressure drops. What would be the volume of the same number of molecules of hydrogen at an altitude of 40km where the pressure is and temperature is 

What is the probability of finding a particle at centre of box in it's first excited state in a infinite potential well ??