Concept explainers
(a)
The de Broglie wavelength of the earth.
(a)
Answer to Problem 47E
The de Broglie wavelength of the earth is
Explanation of Solution
Given Info: The mass of earth is
Write the formula to calculate the de Broglie wavelength of the earth.
Here,
m is the mass of the earth
v is the orbital velocity
Substitute
Conclusion:
Therefore, the de Broglie wavelength of the earth is
(b)
The quantum number of the earth’s orbit.
(b)
Answer to Problem 47E
The quantum number of the earth’s orbit is
Explanation of Solution
Given Info: The circumference of the earth is
Write the expression for the relation between the circumference and wavelength.
Here,
n is the quantum number of earth’s orbit
C is the circumference of the earth’s orbit
Substitute
Conclusion:
Therefore, the quantum number of the earth’s orbit is
(c)
Does the quantum consideration has any major role on the earth’s orbital motion.
(c)
Answer to Problem 47E
The mass of the earth is too big and hence the de Broglie wavelength is too small to detect therefore
Explanation of Solution
Write the formula to calculate the de Broglie wavelength of the earth.
Since the de Broglie wavelength of any object is inversely proportional to the mass of the object. As mass increases the observed de Broglie wavelength is too small to detect. Here the mass of the earth is too big and hence too small the de Broglie wavelength.
In addition to that the value of plank’s constant h has the order of
Conclusion:
Therefore, the mass of the earth is too big and hence the de Broglie wavelength is too small to detect therefore quantum mechanics has no role in the case of earth’s orbit motion.
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