an electron orbiting around hydrogen atom in circular orbit of radius 1armgstrom with the speed of 5*10^6 m/sec. Calculate magnetic field produced at the nucleus?
Why did the electron join the circus? Because it wanted to orbit around the nucleus and become a magnetic field performer! In all seriousness, to calculate the magnetic field produced at the nucleus by an electron orbiting around a hydrogen atom, we can use the formula for the magnetic field of a circular current loop.
The magnetic field produced at the center of a circular loop is given by the equation:
B = (μ₀*I)/(2*R)
Where:
B is the magnetic field
μ₀ is the magnetic constant (4π × 10⁻⁷ Tm/A)
I is the current (in Amperes)
R is the radius of the loop (in meters)
In this case, the current is due to the motion of the electron, which can be calculated using the equation:
I = q*v
Where:
q is the charge of the electron (in Coulombs)
v is the velocity of the electron (in m/s)
The charge of the electron is -1.6 × 10⁻¹⁹ C, and the velocity is given as 5 × 10⁶ m/s. The radius of the circular orbit is 1 Å, which is equivalent to 1 × 10⁻¹⁰ m.
Now we can plug in the values and calculate the magnetic field B:
I = (-1.6 × 10⁻¹⁹ C) * (5 × 10⁶ m/s)
R = 1 × 10⁻¹⁰ m
μ₀ = 4π × 10⁻⁷ Tm/A
Calculating I:
I = (-1.6 × 10⁻¹⁹ C) * (5 × 10⁶ m/s) = -8 × 10⁻¹³ A
Calculating B:
B = (μ₀*I)/(2*R) = (4π × 10⁻⁷ Tm/A) * (-8 × 10⁻¹³ A) / (2 * 1 × 10⁻¹⁰ m)
B = -8π × 10⁻¹¹ T
So, the magnetic field produced at the nucleus by the electron orbiting around the hydrogen atom is approximately -8π × 10⁻¹¹ Tesla.
To calculate the magnetic field produced at the nucleus by an electron orbiting around a hydrogen atom, we can use the formula for the magnetic field due to a moving charge:
B = (μ₀ * q * v) / (4π * r²)
where:
B is the magnetic field produced at the nucleus
μ₀ is the permeability of free space (4π * 10^(-7) T·m/A)
q is the charge of the electron (-1.6 * 10^(-19) C)
v is the speed of the electron (5 * 10^6 m/s)
r is the radius of the circular orbit (1 Å = 1 * 10^(-10) m)
Let's calculate the magnetic field:
B = (4π * 10^(-7) T·m/A * -1.6 * 10^(-19) C * 5 * 10^6 m/s) / (4π * (1 * 10^(-10))^2 m²)
B = (-6.4 * 10^(-26) T*m²/A * m²/s) / (1 * 10^(-20) m²)
B = -6.4 * 10^(-26 - 20) T
B = -6.4 * 10^(-46) T
Therefore, the magnetic field produced at the nucleus by the electron orbiting the hydrogen atom is approximately -6.4 * 10^(-46) T.
To calculate the magnetic field produced by the electron orbiting around the hydrogen nucleus, you can use the formula for the magnetic field due to a moving charged particle.
The formula is given by:
B = (μ0 * q * v) / (4π * r²)
Where:
B is the magnetic field,
μ0 is the permeability of free space (vacuum) with a value of 4π x 10⁻⁷ T·m/A,
q is the charge of the electron (1.6 x 10⁻¹⁹ C),
v is the velocity of the electron (5 x 10⁶ m/s), and
r is the radius of the electron's circular orbit (1 Å = 1 x 10⁻¹⁰ m).
Plug in the given values into the formula:
B = (4π x 10⁻⁷ T·m/A * 1.6 x 10⁻¹⁹ C * 5 x 10⁶ m/s) / (4π * (1 x 10⁻¹⁰ m)²)
Simplifying the equation:
B = (4π x 10⁻⁷ T·m/A * 1.6 x 10⁻¹⁹ C * 5 x 10⁶ m/s) / (4π * 1 x 10⁻²⁰ m²)
The factors of 4π in the numerator and denominator cancel out:
B = (10⁻⁷ T·m/A * 1.6 x 10⁻¹⁹ C * 5 x 10⁶ m/s) / (1 x 10⁻²⁰ m²)
Performing the multiplication:
B = (8 x 5 x 10⁻¹ x 10⁶ x 10⁻²) T
Simplifying further:
B = 4 x 10⁻⁵ T
Therefore, the magnetic field produced at the nucleus by the electron is 4 x 10⁻⁵ Tesla.