What is the wavelength of a 1400 kg truck traveling at a rate of 72 km/h?
Use the de Broglie equation,
wavelength = h/mv
mass in kg, v in m/s, h is Planck's constant.
What is the de Broglie wavelength of an electron (m = 9.11 10-31 kg) moving at a velocity of 3.0 107 m/s (10% of the speed of light)?
14?
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To find the wavelength of a moving object, we need to relate its speed, mass, and wavelength using the de Broglie wavelength formula. The de Broglie wavelength (λ) is given by the equation:
λ = h / p
Where:
λ is the wavelength,
h is the Planck's constant (6.62607015 × 10^-34 J·s),
p is the momentum of the object.
To calculate the momentum (p) of an object, we use the equation:
p = m * v
Where:
p is the momentum,
m is the mass of the object,
v is the velocity of the object.
In this case, the mass of the truck (m) is 1400 kg and the velocity (v) is given as 72 km/h, which needs to be converted to meters per second (m/s).
First, convert the velocity from km/h to m/s:
72 km/h * (1000 m / 1 km) * (1 h / 3600 s) = 20 m/s
Now that we have the velocity in meters per second (v = 20 m/s), we can calculate the momentum (p) of the truck using the equation:
p = m * v
p = 1400 kg * 20 m/s
p = 28000 kg·m/s
Now, we can calculate the wavelength (λ) using the equation:
λ = h / p
λ = (6.62607015 × 10^-34 J·s) / (28000 kg·m/s)
Calculating this gives us the wavelength of the truck.