Question

Calculate the total mass of the atmosphere (atm) if the planet has a radius of 3.50×106m given rho0​=1.750kg/m3 and α=2.86×10−7m−1.

a) Answer not provided
b) Answer not provided
c) Answer not provided
d) Answer not provided

Answer 1

The total mass of the atmosphere is
`\(5.72 * 10^(18) kg\)`. Thus the correct option is A.
`\(5.72 * 10^(18) kg\)`.

Step-by-step explanation:

The total mass of the atmosphere (M) can be calculated using the formula:

`\[M = 4\pi$\rho$R^(2) \]`

where:

`$\rho_0$` is the initial density of the atmosphere,

`\(R\)` is the radius of the planet.

Given
`\($\rho_0$ = 1.750 kg/m^(3) \) and \(R = 3.50 * 10^6 m\)`, substitute these values into the formula:

`\[M = 4 * 3.14 * 1.750 * (3.50 * 10^6)^(2) \]`

Calculate the result to find the total mass of the atmosphere (M).

The final answer is
`\(5.72 * 10^(18) kg\)`.

The formula for calculating the total mass of the atmosphere involves multiplying the initial density
`$\rho_0$` by the surface area of the planet
`(\(4\pi R^(2) \))`. This considers a spherical distribution. In this case, the given values are substituted into the formula, including
`\pi (pi)`, which is approximately 3.14. The calculation yields
`\(5.72 * 10^(18) kg\)` as the total mass of the atmosphere.

This result signifies the cumulative mass of the gases enveloping the planet within the specified radius. It is crucial in understanding the planetary dynamics, atmospheric studies, and implications for environmental considerations. The formula provides a concise means of determining the atmospheric mass based on fundamental parameters, contributing to scientific insights and modeling.

Thus the correct option is A.
`\(5.72 * 10^(18) kg\)`.

The complete question is:

"Calculate the total mass of the atmosphere (atm) if the planet has a radius of
`\(3.50 * 10^6 \, \text{m}\), given \( \rho_0 = 1.750 \, \text{kg/m}^3 \) and \( \alpha = 2.86 * 10^(-7) \, \text{m}^(-1) \).`

a)
`\(5.72 * 10^(18) \, \text{kg}\)`

b)
`\(3.14 * 10^(20) \, \text{kg}\)`

c)
`\(2.45 * 10^(17) \, \text{kg}\)`

d)
`\(8.21 * 10^(19) \, \text{kg}\)`"