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 300 V and then enters a magnetic field with magnitude 0.742 T perpendicular to the path of the ion. What is the radius of the ion's path in the magnetic field?

8.87mm

Step-by-step explanation:

If the singled charged ion accelerates through a magnetic field, the force acting on the ion is expressed as;

F = qvBsin(theta)

Since the magnetic field is perpendicular to the path of the iron, angle that the ion made with the field will be 90°

F = qvBsin90°

F= qvB... (1)

q is the charge on the ion

v is the velocity possessed by the charge

B is the magnetic Field

Also according to Newton's second law, the force experienced by the ion can also be expressed as;

F = ma = mv²/R ... (2)

Where a is the centripetal acceleration = v²/R

m is the mass of the ion

R is the radius

Equating both value of the force to get the radius;

qvB = mv²/R

qB = mv/R

R = mv/qB ...(3)

Given m = 1.16×10^-26kg

q = 1.6×10^-19C

B = 0.742T

v = ?

Before we can get the radius R, we need to get the velocity of the charge in the wire using the relationship.

1/2mv² = eV (since the ion possess kinetic energy and potential difference V)

From the equation, v² = 2eV/m

v = √2eV/m

v = √2×1.6×10^-19×300/1.16×10^-26

v = √8.28×10^9

v = 90971.77m/s

Substituting v = 90971.77m/s into equation 3 to get the radius R of the ion's path in the field will give;

R = mv/qB

R = 1.16×10^-26 × 90971.77/1.6×10^-19×0.742

R = 1.056×10^-21/1.19×10^-19

R = 0.00887m

R = 8.87mm

step-by-step explanation:

we are given

since, we have to isolate x on anyone side

so, we can move all x terms on one side

subtract both sides by 2x

add both sides by 9

divide both sides by 4

we get

step-by-step explanation:

we are given a graph for system of inequalities.

in order to write the system of inequalities for the given graph, we need to find the inequality for each of the line separately.

let us find the slope of dotted line first.

taking two coordinates on the graph.

let us say (0,0) and (3,1).

let us find the slope of the line now.

slope of the dotted line would be =.

y-intercept of dotted line is y=0 only.

plugging slope m= and b=0 in slope-intercept form y=mx+b, we get

.

the line is shaded up of that dotted line.

therefore, for shading up we would take greater than inequality symbol > .

and because it's a dotted line we would take only > symbol in place of = sign in above equation of line.

therefore, inequality for dotted line would be

let us take two points (3,1) and (0,4) on the solid line.

slope of the solid line would be =.

for the solid line we have y-intercept b= 4.

plugging slope m= -1 and b=4 in slope-intercept form y=mx+b, we get

y = -1x + 4.

the line is shaded down of that solid line.

therefore, for shading down we would take less than inequality symbol < .

and because it's a solid line we would take ≤ symbol in place of = sign in above equation of line.

therefore, inequality for solid line would be