Ions of two isotopes with masses 6.5*10^-26 kg and 6.8*10^-26

Ions of two isotopes with masses 6.510^-26 kg and 6.810^-26 kg, accelerated by a potential difference of 0.5 T, fly into a uniform field with an induction of 0.5 T perpendicular to the induction lines. It is necessary to determine the difference in the radii of the trajectories of isotope ions in a magnetic field if the charge of each ion is equal to the electronic charge.

Answer:

Let us write the equation of motion of an ion in a magnetic field:

F = q v B,

where q is the charge of the ion, v is its speed, B is the magnetic field induction.

The force acting on the ion is perpendicular to its speed and directed in a plane perpendicular to the magnetic field induction lines.

The ion velocity modulus can be expressed in terms of the potential difference:

v = sqrt(2qU/m),

where U is the potential difference, m is the mass of the ion.

Then the radius of the ion trajectory can be expressed in terms of its speed:

R = mv/qB.

Substituting the expression for speed, we get:

R = sqrt(2mU)/qB.

Let's calculate the radii for each isotope:

R1 = sqrt(26,510^-260,5)/(1,610^-19*0.5) ≈ 0.291 m.

R2 = sqrt(26,810^-260,5)/(1,610^-19*0.5) ≈ 0.303 m.

Answer: the difference in the radii of the trajectories of isotope ions in a magnetic field is approximately 0.012 m.

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Welcome to our digital goods store! We present to you a digital product - a unique product that will allow you to expand your knowledge in the field of physics and magnetic fields.

Our digital product contains a solution to problem 30670, which describes the movement of ions of two isotopes with masses 6.510^-26 kg and 6.810^-26 kg, accelerated by a potential difference of 0.5 T, in a uniform magnetic field with an induction of 0.5 T, perpendicular to the induction lines.

The problem requires determining the difference in the radii of the trajectories of isotope ions in a magnetic field if the charge of each ion is equal to the electronic charge.

In our product you will find a detailed description of the solution to the problem, including a brief record of the conditions, formulas and laws used in the solution, the derivation of the calculation formula and the answer.

You will also have the opportunity to study the problem in a beautiful html format on any device and expand your knowledge in the fascinating field of physics.

If you have any questions about the solution, our specialists are always ready to help. By purchasing our digital product, you get a unique opportunity to expand your horizons and learn something new in the field of magnetic fields.

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Product description:

Ions of two isotopes with masses 6.510^-26 kg and 6.810^-26 kg, accelerated by a potential difference of 0.5 V, fly into a uniform magnetic field with an induction of 0.5 Tesla perpendicular to the induction lines. The charge of each ion is equal to the electronic charge.

To solve the problem, it is necessary to use the formula for the radius of the particle trajectory in a magnetic field:

r = mv/qB

where r is the radius of the trajectory, m is the mass of the particle, v is the speed of the particle, q is the charge of the particle, B is the magnetic field induction.

Using this formula, we can express the radii of trajectories for ions of both isotopes:

r1 = (m1v)/qB = (6,510^-26 kg * sqrt(2q0.5 V/m1)) / q * 0.5 Tl = 4.1510^-3 m r2 = (m2v)/qB = (6,810^-26 kg * sqrt(2q0.5 V/m2)) / q * 0.5 T = 4.2610^-3 м

where m1 and m2 are the masses of the first and second isotopes, respectively.

Thus, the radii of trajectories for isotope ions will differ by 0.11*10^-3 m.

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