Booklet 2A - Particles (Worked Examples)

Question 1

The height of the Eifel Tower is 301m.
An average human hair is about 50 μm thick.

How many orders of magnitude is the Eifel Tower larger than the thickness of a human hair?

Answer 1

The height of the Eifel Tower is 3.01 x 10² m. This is an order of magnitude 2.
The thickness of a human hair is 5 x 10^-5 m.This is an order of magnitude -5.
The Eiffel Tower is 2 - (-5) = 7 orders of magnitude larger than a human hair.

Question 2

The mass of a proton is 1.673 x 10^-27 kg
Show that the mass-energy equivalence of a proton is 941 MeV.
(1 eV = 1.6 x 10 ^-19 J)

Answer 2

E = ?
m = 1.673 x 10^-27 kg

E = mc²
E = 1.673 x 10^-27 x (3 x 10⁸)²
E = 1.5057 x 10^-27 (J)

Convert to eV
E = 1.5057 x 10^-27 / 1.6 x 10 ^-19
E = 941,062,500 eV
E = 941 MeV

Question 3

A proton is accelerated from rest through a potential difference of 10 V.

(a) Calculate the electric potential energy gained.
(b) Calculate the speed of the proton at the end.

Answer 3

V = 10 V
Q = 1.6 x 10<sup>-19</sup> C (from data sheet)
m = 1.673 x 10<sup>-27</sup> kg (from data sheet)

(a) W = QV
= 1.6 x 10^-19 x 10
= 1.6 x 10^-18 J

(b) E_k = ½mv²
1.6 x 10^-18 = ½ x 1.673 x 10^-27 x v²
v = 4.37 x 10⁴ ms^-1

Question 4

Complete the following nuclear equation for alpha emission:

²²⁴₈₈Ra ⇒ ⁴₂He + X

Answer 4

224 - 4 = 220

88 - 2 = 86

From periodic table 86 is the atomic number for Radon (Rn)

X is ²²⁰₈₆Rn

Question 5

Mistake in scan! mass of Mo is 162.5 x 10^-27​ kg

Answer 5

Question 6

Answer 6