Surname 9 Essay Example

Q.1 (4.55 x ) x (4.23 x ) = 0.32 x s

Speed = 2.24 x s; hence depth of water = (0.32 x ) x (2.24 x

Depth = 71.68 m

Parallel rays of a monochromatic light of wavelength λ as shown in the figure above are incident on a diffraction grating, which has a slit separation distance of d.  If the grating has m lines per metre, the grating spacing is given by: d =

The rays are diffracted at an angle θ to the normal of the adjacent slits. Light from A must be in phase with light from B. Hence; 

                                                AC = mλ, where m = 0, 1, 2, 3…

                                            AC = d sin θ

                                                d sin θ = mλ

Simplifying the equation; sinθ =

Q.3 (b) sin θ =
where
θ = angle = 15^o

slit distance = ; slit per mm= 400 ; hence slit per cm = 400000

taking order of magnitude = 1 ; slit distance = = 2.5 x

wavelength (λ)=
=
= 6.47 x m

(c) number of orders visible =

= = 1 order

5. (iii) E = hf

Where E = energy of an electron, h= plancks constant = 6.62 x J/s

f= frequency = 8.80 x Hz

E = (6.63 x ) x (8.80 x ) = 5.834 x J

Work function of metal = 2.6eV = (1.6 x x (2.6) = 4.16 x J

Since the energy of the light is more than the work function of the metal, electrons will be dislodged from the metal.

6. (b) (i). h =

Where h = plank’s constant

= change in energy of electron = (3 – 1)eV= 2eV = (1.6 x x (2)

= 3.2 x J

= change in frequency = (12 – 7) X = 5 x Hz

h = = 6.4 x whereas the ideal plank’s constant is 6.63 x

(ii) work function = hf = 6.4 x x 4.39 x = 2.81 x J

(iii) Energy of electron = work function + kinetic energy

hf = wf + ke ; 6.4 x x 5 x = 2.81 x + ke;

Ke = ; (3.2 x — (2.81 x = 0.39 x

Ke= mv² where m= mass of electron= 9.1 x and V = velocity of electron

V == 2.93 x m/s

(ii)
since h= eV, this shows that wavelength is inversely proportional to the accelerating potential. Thus shorther wavelength X-rays are produced by increasing the accelerating potential difference.

hf= h= eV where h = plank’s constant = = 6.63 x c= velocity of x-ray = 3 x m/s

eV= 50 x x 1.6 x = 8 x

λ = = = 2.49 x m

(iii) increase in acceleration potential in the x-ray would lead to an increase in the x ray intensity, increase in value of characteristic radiation and also a lower short wavelength limit

8. (a) kinetic energy = potential energy = q* v = ; (1.6 x ) x (6 x )= 9.6 x

K.e = mv² = 9.6 x

where m= mass of electron= 9.1 x and V = velocity of electron

V == 1.45 x m/s

(b) De Broglie wavelength (λ) = = where h = plank’s constant = 6.63 x

m= mass of electron = 9.1 x and V = velocity of electron = 1.45 x m/s

λ =
= 5.025 x

Works cited

Born, Max, and Emil Wolf. “Principles of optics: electromagnetic theory of propagation,

interference and diffraction of light.” 7th expanded edition. Cambridge: Cambridge

University Press, 1999. 28-40

Bragg, William Henry, and William Lawrence Bragg. “X rays and crystal structure”. 4th ed.

London: G. Bell and Sons, ltd., 1924. 12-23

Compton, Arthur Holly, and Samuel King Allison.” X-rays in theory and experiment,” New

York: D. Van Nostrand company inc., 1935. 48-51

Cowley, J. M. “Diffraction physics” 2nd, rev. ed. Amsterdam: North-Holland Pub. Co. 1981.

Hammond, C. “The basics of crystallography and diffraction.” 2nd ed. Oxford: Oxford

University Press, 2001. 50-62