It is 8 kilograms. I had to provide more text, so here it is.
The formula to apply is expressed as:
ρ = nA/VcNₐ
where
ρ signifies density
n represents the number of atoms within a unit cell (for FCC, n=4)
A indicates the atomic weight
Vc stands for the cubic cell volume equal to a³, with a being the side length (for FCC, a = 4r/√2, where r is the radius)\
Nₐ denotes Avogadro's number, which is 6.022×10²³ atoms/mol
Calculating the radius: r = 0.1387 nm*(10⁻⁹ m/nm)*(100 cm/1m) = 1.387×10⁻⁸ cm
Then find a: a = 4(1.387×10⁻⁸ cm)/√2 = 3.923×10⁻⁸ cm
Then calculate V: V = a³ = (3.923×10⁻⁸ cm)³ = 6.0376×10⁻²³ cm³
Now compute density:
ρ = [(4 atoms)(195.08 g/mol)]/[(6.0376×10⁻²³ cm³)(6.022×10²³ atoms/mol)]Finally, we get ρ = 21.46 g/cm³
The maximum depth at which he could still breathe, given the pressure of -74 mm Hg, equates to 0.98 m. Pressure of -74 mm Hg translates to 9605 Pa or 9709 N/m². With the density of water set at 1000 kg/m³, we can utilize the pressure equation P = rho g h to determine h, deriving that h = 0.98 m.
<span>The work done corresponds to the potential energy that the person acquires while ascending the stairs.
work = potential energy acquired = mgh
W = 75kg * 9.8m/s² * 2.50m = 1837.5 J</span>
Impulse can be equated to the force associated with momentum change, expressed as F*t = mv - mu
Given the mass and speed values are provided, apply the formula from the right-hand side:
mass, m = 1.7 x 10^27 kg
initial velocity, u = 0.991 x (3 x 10^8) = 2.973 x 10^8
final velocity, v = 0.994 x (3 x 10^8) = 2.982 x 10^8
Consequently, the calculation is:
Impulse = mv - mu
= [(1.7 x 10^27) x (2.982 x 10^8)] - [(1.7 x 10^27) x (2.973 x 10^8)]
= (5.0694 x 10^35) - (5.0694 x 10^35)
= 0
