Given that a proton of mass 1.6726 × 10-27 kg has a wavelength of 2.426*10-10 m, calculate the velocity of the proton.
To calculate the velocity of the proton, we can use the de Broglie equation:
wavelength = h / (mass * velocity)
where:
- wavelength is the given wavelength of the proton (2.426 * 10^(-10) m)
- h is the Planck's constant (6.62607015 × 10^(-34) J·s)
- mass is the mass of the proton (1.6726 × 10^(-27) kg)
- velocity is the unknown velocity of the proton
Rearranging the equation, we can solve for velocity:
velocity = h / (mass * wavelength)
Substituting the given values:
velocity = (6.62607015 × 10^(-34) J·s) / ((1.6726 × 10^(-27) kg) * (2.426 * 10^(-10) m))
Calculating this expression will give us the velocity of the proton.
To calculate the velocity of the proton, we need to use the de Broglie wavelength equation, which relates the wavelength of a particle to its velocity. The equation is given as:
λ = h / mv
Where:
λ is the wavelength,
h is the Planck's constant (6.62607015 × 10^-34 Js),
m is the mass of the proton (1.6726 × 10^-27 kg),
v is the velocity.
Now, let's rearrange the equation to solve for v:
v = h / (mλ)
Plugging in the values:
v = (6.62607015 × 10^-34 Js) / ((1.6726 × 10^-27 kg) * (2.426*10^-10 m))
Now, we can calculate the velocity by dividing the numerator by the denominator:
v ≈ 1.09 × 10^6 m/s
Therefore, the velocity of the proton is approximately 1.09 × 10^6 m/s.
de Broglie's wave equation ... λ = h m v ... v = λ / (h m)
h is Planck's constant ... 6.626 × 10-34 m2 kg / s
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