The velocity of an electron in the ground state of hydrogen atom is 2....
The velocity of an electron in the ground state of hydrogen atom is 2....
**Velocity of an electron in the ground state of hydrogen atom**
The velocity of an electron in the ground state of a hydrogen atom is given as 2.2 × 10^6 m/s.
**De Broglie wavelength associated with a particle**
According to the De Broglie hypothesis, every particle with momentum has a corresponding wavelength associated with it. The De Broglie wavelength (λ) is given by the equation:
λ = h/p
Where:
λ is the De Broglie wavelength,
h is the Planck's constant (6.626 × 10^-34 J·s),
p is the momentum of the particle.
**Comparing the electron and muon**
The muon is a subatomic particle with a mass (mμ) that is 207 times greater than the mass of an electron (me). We need to compare the De Broglie wavelength of the muon in the ground state of muonic hydrogen to that of the electron in the ground state of hydrogen.
**Finding the momentum of the electron**
To find the momentum of the electron, we use the equation:
p = mv
Where:
p is the momentum,
m is the mass of the electron,
v is the velocity of the electron.
**Finding the momentum of the muon**
The momentum of the muon (pμ) can be calculated using the equation:
pμ = mμvμ
Where:
pμ is the momentum of the muon,
mμ is the mass of the muon,
vμ is the velocity of the muon.
**Calculating the De Broglie wavelength of the electron**
Using the equation λ = h/p, we can calculate the De Broglie wavelength of the electron by substituting the values of h and p.
**Calculating the De Broglie wavelength of the muon**
Using the equation λ = h/pμ, we can calculate the De Broglie wavelength of the muon by substituting the values of h and pμ.
**Comparing the De Broglie wavelengths**
Finally, we compare the De Broglie wavelengths of the electron and the muon to determine the relationship between them based on their masses and velocities.
**Conclusion**
In conclusion, the De Broglie wavelength associated with a muon in the ground state of muonic hydrogen can be calculated by comparing it to the De Broglie wavelength of an electron in the ground state of hydrogen. The muon has a greater mass than the electron, so its momentum and De Broglie wavelength will be different. The specific value of the muon's De Broglie wavelength can be calculated using the given mass ratio and velocity.
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