Question

1. When light behaves like a wave, the equation c = λν is used.

a) Name each variable in the equation.

b) What are the units of each variable?

c) The equation above can be rearranged to ν = c / λ . What does that tell you about the relationship between λ and ν ?

2. Light can behave as a particle, which can be thought of as a 'bundle' of light referred to as a photon of light. Each photon of light has the energy: Ephoton = hν .

a) Name each variable in the equation.

b) What are the units of each variable?

c) What is the energy of 100 photons of light?

d) What is the relationship between E and ν according to the equation?

e) Replace the variable ν with the equation for ν part (1.c). What is the relationship between E and λ ?

f) Look at the two waves below and label each as having low/high energy and low/high frequency

3. Four quantum numbers are assigned to each electron: n, l, ml , ms .

Define each quantum number: what do they mean, and what are their allowed values?

a) n

b) l

c) ml

d) ms

4. Describe the rules for filling orbital energy diagrams:

a)

b)

c)

Answer 1

1. c = λν

(a) In this equation c is speed of light, λ is wavelength of electromagnetic radiation and ν is fequency of electromagnetic radiation.

(b) c has fixed value i.e., 3.0 x 108 m/s

     λ (wavelength) is measured in metre (m)

and ν (frequency) is measured in Hz or s^-1

(c) From the expression ν = c / λ we can say that v and λ are inversely proportional to each other. If v increases λ decreases and vice versa.

2. E_photon = hν

(a) In the above equation E is energy of photon, h is planck's constant and v is frequency

(b) Unit of E = Joule (J)

      Planck's constant = 6.626 x 10^-34 J s

      v = s^-1

(c) Energy of 1 photon E = hν

Therefore energy of 100 photon E = 100hν

Frequency and h are constant we can also energy of 100 photon is 100E

(d) According to the equation E and v are directly proportional.

(e) ν = c / λ, put this value of v in equation E_photon = hν , we get

E_photon = hc / λ

Here we can E and λ are inversely proportional.

3. (a) n is principle quantum number identifies the principle shell, n = 1,2,3,....

    (b) l is azimuthal quantum number provides information about the sub-shells , i =0,1,2.....,(n - 1)

    (c) ml is Magnetic orbital quantum number gives information about the spatial orientation of the orbitals with respect to standard set of co-ordinate axis, ml = -l, -(l-1), -(l-2)....0,1,....(l-2), (l-1),l. ml has 2l+1 values for any subshell l.

   (d) ms is electron spin quantum number gives infirmation about the spin of the electron in any orbital, ms= -1/2 or +1/2

4. Rules for filling orbital energy diagrams

Filling of electrons into the orbitals takes place according to the aufbau principle which is based on Pauli's exclusion principle, Hund's rule and relative energy of the orbitals

Electron first occupy the lowest energy orbital available to them and enter into higher energy orbitals only after the lower energy orbitals are filled.

No two electron in an atom can have same set of 4 quantum numbers.

No two electron mayexist in same orbital with same spin.

Max. number of electron in the principle shell = 2n²