CML 511 Quantum Chemistry: Tutorial 3, Due date: 6th Sep 2024, 9 am I sem, 2024-25 1. A particle of mass m is confined to a one-dimensional box of length L. Calculate the probability of finding it in the following regions: (a) 0 ≤ x ≤ ½-½ 4, (b) 0 ≤ x ≤ ≤L, (c) L - 8x ≤ x ≤L + 8x. Derive expressions for a general value of n. Then evaluate the probabilities (i) for n = 1, (ii) in the limit n co. Compare the latter to the classical expectations.

Imagine a world in which the rule for the l quantum number is that values start with 1 and go up to n. The rules for the n and mi quantum numbers are unchanged from those of our world. Write the quantum numbers for the first two shells (i.e., n = 1 and n = 2).

Selenium atoms have a particular transition that emits light of frequency 1.53 1015 Hz. (Hz is the abbreviation for hertz, which is equivalent to the unit/s, or s1.) Is this light in the visible spectrum? If so, what is the color of the light? (See Figure 7.5.)

In a FranckHertz experiment on sodium atoms, the first excitation threshold occurs at 2.103 eV. Calculate the wavelength of emitted light expected just above this threshold. (Note: Sodium vapor lamps used in street lighting emit spectral lines with wavelengths 5891.8 and 5889.9 Å.)

Radio waves in the AM region have frequencies in the range 530 to 1700 kilocycles per second (530 to 1700 kHz). Calculate the wavelength corresponding to a radio wave of frequency 1.460 106/s (that is, 1460 kHz).

Consider burning ethane gas, C2H6 in oxygen (combustion) forming CO2 and water. (a) How much energy (in J) is produced in the combustion of one molecule of ethane? (b) What is the energy of a photon of ultraviolet light with a wavelength of 12.6 nm? (c) Compare your answers for (a) and (b).

6.9 If a string of decorative lights includes bulbs with wave-lengths of 480, 580, and 700 mm, what are the frequencies of the lights? Use Figure 6.6 to determine which colors are in the set.

How does probability fit into the description of the atom?

A lightbulb radiates 8.5% of the energy supplied to it as visible light. If the wavelength of the visible light is assumed to be 565 nm, how many photons per second are emitted by a 75-W lightbulb? (1W=1J/s)