Question

Please explain each step as thoroughly as you can as I am quite confused with this unit. Thanks in advance!

1. A gas in a container is at a constant temperature T. The molecules have two vibrational energy states, the higher of which has energy 0.88 k_BT. There are 3000 molecules in this higher energy state and approximately 5500 in the lower state. What is the energy of the molecules in the lower state?

2. Spherical particles have a density of 1.30 × 10³ kg m³ and radius of 0.22 × 10⁶ m.
(a) What is their mass?
(b) What is their apparent weight in water??

Answer 1

2)

a)

mass = volume x density

m = (4/3)*pi*r^3 x $\rho$

m = (4/3) x pi x (0.22 x 10^-6)^3 x 1.30 x 10^3

m = 5.8 x 10^-17 kg

b)

Apparent weight = Weight - Weight of displaced fluid

Mass of displaced water = (4/3)*pi*r^3 x $\rho$

= (4/3) x pi x (0.22 x 10^-6)^3 x 1000

= 4.46 x 10^-17 kg

apparent weight =  5.8 x 10^-17 kg - 4.46 x 10^-17 kg

apparent weight = 1.3 x 10^-17 N