Answers to revision questions

Post: Unit 3: Radiation and matter - why are waves so important in Physics?

Words to the effect of: Because the wave only contains up/down motion, so any single point on it can only move up and down, even though the wave oscillation itself is travelling sideways or forwards.

Energy, in form of motion. Just motion won't work, it's important to get that the motion is a way of moving energy.

Similarities: They are both electromagnetic waves, they are both travelling at the same speed, they are both generated by something oscillating.

Differences: They have different wavelengths, they have different frequencies.

Post: Frequency, Wavelength, Amplitude, and Period


Be careful with the use of decimal points and units here. All lengths need putting as meters. 1 nanometer = 0.000000001 meters, and lightspeed is 300,000,000 meters per second, so the equation....

....(where V is wavespeed and lambada is wavelength) should be applied:
f = 300,000,000 / 0.000000450 = 666666666666666.66666666666666667 Hertz

450 nanometers = 666,666,666,666,666.7 Hertz
570 nanometers = 526,315,789,473,684.2 Hertz
900 nanometers = 333,333,333,333,333.3 Hertz

For this we use the equation...

....where p is period, and f is frequency. First we re arrange the equation to get... f = 1/2, or 1/2 a Hertz. We can then use ....

1/2 =  V/ 20

1/2 x 20 = V

V = 10 meters / second

The trick to this - which is a useful exam skill - is to pick up on the description of radio waves as 'electromagnetic waves'. We've already been told that all electromagnetic waves travel at a speed of 300,000,000 meters per second, so we can use good old....

f = 300,000,000 / 10
f = 30,000,000 Hertz

a: F is frequency, V is wavespeed, and Lambada is wavelength

Post: Phase, coherence, and seasick cat.


a) Wave set A is coherent. Wave set B is coherent (the amplitudes are different but still similar).

b) Wave set B is also in phase.

a) 90 degrees

b) also 90 degrees, the waves are coherent so the phase difference doesn’t change.

3) 360 degrees (one peak to the next peak, passing through one trough, so one complete wave which is 360 degrees of phase)

Radioactivity and half life revision questions:

Important note: If you put the wrong unit, or don’t put down any unit, you don’t get a mark! Examiners will do that, so I have to too. Go back and re check your units before you mark.


Gamma rays go through metal sheets but are stopped by lots of dense material like lead, so source A is giving off gamma rays. Beta rays go through air easily but are stopped by thin aluminium, so source B is giving off beta rays. Alphas are puny and get stopped by air, so source C is giving off alphas.


a: It’s easiest to draw out the table:


Percentage of original activity











So it takes 4 half-lives.

b: Looking at the table we see it takes 2 half-lives for the activity to reach 25%. 1 half-life is 23 second, so the answer is 2 x 23 = 46 seconds.


a: This question wants absorbed dose, so we need to use:


(D is absorbed dose, E is energy, and m is mass)

D = 50 joules / 4kg

D= 12.5 Greys (this is probably bad for the cat)

b: This question asks for equivalent dose, so we need to use

(H is equivalent dose, D is the absorbed dose, W is the weighting factor)

H = 12.5 Greys x 20

H = 250 Sieverts (Either the cat is dead, or you now have a Hulk-cat)

4: The question asks for the activity in Becqurels, so  we want the equation:


Where A is activity in Becquerel’s, N is the number of atoms that decayed, and t is the time in seconds their decay took.

A = 10,000,000 / 2 = 5,000,000 Becquerel’s

Critical angle and total internal reflection:

Both questions need us to use the equation:

Where n1 is the refractive index of the medium the light is entering, and and n2 is the refractive index of the medium the light is leaving
Well break the maths into two stages: First the bit inside the brackets...
1/ 1.3 = 0.7692307692307692
....then the bit outside them.....
Sin-1 (0.7692307692307692) = 50.285 degrees, or 50.3 degrees to 3 significant figures
2 :
The ray is now leaving a material with a lower refractive index (the water) for a medium with a higher one (glass) so total internal refraction cannot occur. 


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