A singly charged ion of 7Li (an isotope of lithium) has a mass of 1.16×10−26 kg. It is accelerated through a potential difference of 250 V and then enters a magnetic field with magnitude 0.878 T perpendicular to the path of the ion. What is the radius of the ion's path in the magnetic field?

Radius = 6.877mm

Step-by-step explanation:

From the question, we have a single charged ion of 7Li with;

Mass(m) = 1.16 × 10^(−26) kg

Potential difference(V) = 250 V

Electron charge of e = 1.6 x 10^(-19)

To solve this question, we'll equate the kinetic energy to potential energy. Thus;

(1/2)(mv²) = eV

Thus;

Velocity (v) =√(2eV/m)

v = √((2 x 1.6 x 10^(-19) x 250)/1.16 × 10^(−26))

v = √(689.655 x 10^(7) = 8.3 x 10⁴ m/s

Since it enters a magnetic field with magnitude B = 0.874 T perpendicular to the path of the ion, thus θ = 90°

Now,we know that;

F = qvBsinθ

Thus F = qvBsin(90)

Sin 90° = 1 ; thus, F =qvB

Also, from Newton's second law, F=ma, also, we know that radial acceleration a = v²/r

So F = mv²/r

Thus equating the 2 forces, we have ;

qvB = mv²/r

So making r the subject, we have;

r = mv/qB = (1.16 × 10^(−26) x 8.3 x 10⁴)/(1.6 x 10^(-19) x 0.874)

= 6.877 x 10^(-3)m = 6.877mm

ratios represent a pattern or relationship that can be scaled.

equivalent ratios are pairs of ratios that represent the same relationship between quantities, and can be generated by multiplying or dividing both quantities in the ratio by the same factor.

in this lesson, students will use double number lines and ratio reasoning to solve ratio problems. by partitioning double number lines into proportionate intervals, students will build an understanding of equivalent ratio relationships as those that are generated by multiplying or dividing two related quantities by the same number. this lesson will build upon students' prior understanding of multiplicative comparisons, number line reasoning and equivalent fractions (while highlighting the difference between equivalent fractions and equivalent ratios); and will build toward future work in this unit on building ratio tables, and work in future grades in proportionality, scaling, and expressing and graphing linear functions.

step-by-step explanation:

ratios represent a pattern or relationship that can be scaled.

equivalent ratios are pairs of ratios that represent the same relationship between quantities, and can be generated by multiplying or dividing both quantities in the ratio by the same factor.

in this lesson, students will use double number lines and ratio reasoning to solve ratio problems. by partitioning double number lines into proportionate intervals, students will build an understanding of equivalent ratio relationships as those that are generated by multiplying or dividing two related quantities by the same number. this lesson will build upon students' prior understanding of multiplicative comparisons, number line reasoning and equivalent fractions (while highlighting the difference between equivalent fractions and equivalent ratios); and will build toward future work in this unit on building ratio tables, and work in future grades in proportionality, scaling, and expressing and graphing linear functions.