The bond between protons and neutrons inside the atomic nucleus is formed by the strong interaction. In classical terms, we can think of it as protons and neutrons exchanging a "meson," a kind of fundamental particle between them. Let's estimate the range of the interaction that's caused by exchange of the π meson which has mass of approximately 2.5×10^-28 kg and decays. To do this, note that from the uncertainty principle one can estimate the lifetime t of a particle of mass m by t=ℏ/(2mc^2)where ℏ=1.05×10^-34 J/s is known as the (reduced) Planck's constant and c=3×10^8 m/s is the speed of light.
Express your answer in femtometers 1 fm=10^-15 m.
Details and assumptions
Nothing can travel faster than the speed of light.
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Distance= speed x time
nick, thank you so much
how do we calculate speed ? time i know
To estimate the range of the strong interaction caused by exchange of the π meson, we need to find the maximum distance it can travel before decaying.
Given:
Mass of the π meson, m = 2.5 × 10^-28 kg
Planck's constant, ℏ = 1.05 × 10^-34 J/s
Speed of light, c = 3 × 10^8 m/s
Using the uncertainty principle, we can estimate the lifetime of the particle (t) using the equation:
t = ℏ / (2mc^2)
Let's substitute the given values into the equation:
t = (1.05 × 10^-34 J/s) / (2 * 2.5 × 10^-28 kg * (3 × 10^8 m/s)^2)
Simplifying the equation:
t = (1.05 × 10^-34 J/s) / (2 * 2.5 × 10^-28 kg * 9 × 10^16 m^2/s^2)
t = (1.05 × 10^-34 J/s) / (4.5 × 10^-12 kg m^2/s^2)
Expressing the time in seconds:
t = 1.05 × 10^-34 J / (4.5 × 10^-12 kg m^2/s^2)
t = 1.05 × 10^-34 / 4.5 × 10^-12
t = 2.33 × 10^-23 s
Now, let's find the distance traveled by the π meson during its lifetime. Since speed equals distance divided by time, we can rearrange the equation:
distance = speed * time
distance = c * t
distance = (3 × 10^8 m/s) * (2.33 × 10^-23 s)
distance ≈ 6.99 × 10^-15 meters
The range of the interaction caused by the exchange of the π meson is approximately 6.99 femtometers (fm).