7.2 When an electron is accelerated through a potential dif- ference A it acquires a kinetic energy eдo. Calculate the mo- mentum, and hence the de Broglie wavelength, of an electron accelerated from rest through (a) 1.00 V, (b) 1.00 kV, (c) 100 kV.

What are the values of E, L, and Lz for an F8+ atom whose electron has the following wavefunctions, listed as n,l,ml? a 1,0,0 b 3,2,2c 2,1,1d 9,6,3.

The maximum in the blackbody radiation intensity curve moves to shorter wavelength as temperature increases. The German physicist Wilhelm Wien demonstrated the relation to be max1/T . Later, Planck’s equation showed the maximum to be max=0.20hc/kt . In 1965, scientists researching problems in telecommunication discovered “background radiation” with maximum wavelength 1.05 mm (microwave region of the EM spectrum) throughout space. Estimate the temperature of space.

The Lyman series of spectral lines for the H atom, in the ultraviolet region, arises from transitions from higher levels to n = 1. Calculate the frequency and wavelength of the least energetic line in this series.

The wave function of an electron in the lowest (that is, ground) state of the hydrogen atom is (r)=( 1 a 0 3 )1/2exp(r a 0 )ao=0.5291010m (a) What is the probability of finding the electron inside a sphere of volume 1.0pm2 , centered at the nucleus (1pm=1012m) ? (b) What is the probability of finding the electron in a volume of 1.0pm2 at a distance of 52.9 pm from the nucleus, in a fixed but arbitrary direction? (c) What is the probability of finding the electron in a spherical shell of 1.0 pm in thickness, at a distance of 52.9 pm from the nucleus?

A particle of mass m is placed in a three-dimensional rectangular box with edge lengths 2L, L, and L. Inside the box the potential energy is zero, and outside it is infinite; therefore, the wave function goes smoothly to zero at the sides of the box. Calculate the energies and give the quantum numbers of the ground state and the first five excited states (or sets of states of equal energy) for the particle in the box.

The given wave function for the hydrogen atom is y =w,00 +210 + 3y2 · Here, ypim has n, 1, and m as principal, orbital, and magnetic quantum numbers respectively. Also, yim an eigen function which is normalized. The expectation value of L in the state wis, is 9h? (a) 11 (b) 11h? 20 (c) 11 (d) 21ħ?

(c) Given that the following kinetic energies were observed for photoejected electrons irradiated by radiation of the wavelengths noted. € (ii) (iii) A (nm) Ek (eV) 320 1.17 360 385 0.885 0.735 0.511 330 345 1.05 Calculate the value of the work function. Calculate the Planck's constant. Describe the experimental features/characteristics of the photoelectric effect. (6) (4) (3)

(a) The position of an electron is known to be within 10 Å(1.0 × 10-9m). What is the minimum uncertainty in itsvelocity component in this direction?(b) Repeat the calculation of part (a) for a helium atom.

Calculate the probability that an electron wi ll be found (a)between x= 0.1 and 0.2 nm, (b) between 4.9 and 5.2 nm in abox of length L = 10 nm when its wavefunction is 'If= (2/L) 112sin(2nx/L). Treat the wavefunction as a constant in the smallregion of interest and interpret 15 Vas llx.