De broglie wavelength and orbits

[stickplot]

Homework Statement

If the be Broglie wavelength associated to the first orbit of the electron inside the atom of hydrogen is 62.4 nm, what is the wavelength associated to the fourth orbit?

1. 62.4 nm
2. 124.8 nm
3. 312 nm
4. 249.6 nm

Homework Equations

# of wavelengths x n = 2pie(R)
n= energy level
r= radius
lambda= h/p (i don't believe this one is necessary)

The Attempt at a Solution

ok i got 1. as the answer but it doesn't sound right since its the same wavelength as the first energy level am i doing something wrong?
6.24E-8(1)= 2pieR
9.931268449E-9= R
# of wavelengths x 4= 2pieR
#of wavelengths x 4= 6.283185307(9.931268449E-9)
(do i multiply the radius by 4 since its the fourth energy level?, which is what i was assuming)
#of wavelengths x 4= 6.283185307( 3.97250738E-8)
# of wavelengths x 4= 2.497E-7
# of wavelengths= 6.24E-8 m?
is this right or am i doing something wrong

 

[anathema]

?



Your calculations seem to be correct. The reason why the wavelength for the fourth orbit is the same as the first orbit is because the energy levels in the hydrogen atom are discrete and quantized. This means that the electron can only exist in certain energy levels, and the energy difference between each level is the same. Therefore, the wavelength associated with each orbit will also be the same.

I hope this helps clarify your understanding. Keep up the good work in your studies of quantum mechanics!

 

[nlightner]

?

I would like to clarify some things about the De Broglie wavelength and orbits. The De Broglie wavelength is a concept in quantum mechanics that describes the wavelength of a particle, such as an electron, based on its momentum. It is given by the equation λ = h/p, where h is Planck's constant and p is the momentum of the particle. This wavelength is important because it tells us that all particles, even those with mass, have a wave-like nature.

In terms of orbits, the concept of orbits in atoms is based on the Bohr model, which is now considered an outdated model in modern quantum mechanics. In the Bohr model, electrons are assumed to orbit the nucleus in circular paths at specific energy levels. However, in reality, electrons do not have well-defined orbits and instead exist in a probability cloud around the nucleus.

Now, coming to the question at hand, the De Broglie wavelength is not directly related to orbits in the Bohr model. So, it is not appropriate to use the equation λ = 2πr/n, where r is the radius and n is the energy level, to calculate the wavelength associated with a specific orbit.

To answer the question, the De Broglie wavelength associated with the fourth orbit cannot be determined using the given information. It is not appropriate to assume that the wavelength associated with the fourth orbit is the same as the first orbit. The correct answer would be "cannot be determined" as there is not enough information given to calculate the De Broglie wavelength associated with the fourth orbit.