It can be shown that the approximate age of the universe is $1 / H$, where $H$ is the Hubble constant Taking $H = 20 \frac { \mathrm { km } / \mathrm { s } } { \mathrm { Mly } }$, estimate the age of the universe, in years. (1 ly $\left. = 9.46 \times 10^{15} \mathrm {~m} \right)$
A) 15 billion years
B) 15 million years
C) 15 thousand years
D) 50 billion years

Question

Quizplus · Accepted Answer

The Hubble constant $H = 20 \frac{\text{km/s}}{\text{Mly}}$ can be used to estimate the age of the universe as $1 / H$. First, convert $H$ to consistent units: $20 \frac{\text{km}}{\text{s}} \cdot \frac{1 \text{ Mly}}{9.46 \times 10^{15} \text{ m}}$. Since $1 \text{ Mly} = 9.46 \times 10^{15} \text{ m}$ and $1 \text{ km} = 1000 \text{ m}$, $H = 20 \times 1000 / (9.46 \times 10^{15}) \text{ s}^{-1}$. To find the age in seconds, take the inverse of $H$, then convert seconds to years ($1 \text{ year} \approx 3.15 \times 10^7 \text{ s}$). This calculation gives an age of approximately 15 billion years.

It Can Be Shown That the Approximate Age of the Universe