In one type of mass spectrometer, ions having the same velocity move through a uniform magnetic field. The spectrometer is being used to distinguish 12 C+ and 14 C+ ions that have the same charge. The 12 C+ ions move in a circle of diameter 25 cm.(a) What is the diameter of the orbit of 14 C+ ions?(b) What is the ratio of the frequencies of revolution for the two types of ion?

A) The diameter of the orbit of 14C+ ions= 29cm

B.) 1.17

Explanation:

A)

Given the diameter of circle 12C ions is d12 = 25

Therefore, we now have to apply the second law to an ion moving in a circle. The acceleration is that of uniform circular motion.

a1= v^2/r

= F/m

=\q\vb/ m equation (1)

Charge q, speed v, and field B are the same for both ions therefore radius must be directly proportional to the mass.

There r is directly proportional to m

d14/ d12 = r14/ r12

= m14 / m12

To calculate the diameter of the orbit of 14C+ ions, we solve for d14.

d14 is given as

d14= m14/m12 × d12

d14= 14u/ 12u × (25cm)

d14= 29 cm

B.) The frequency is equal to the field divided by the circumference.

F12/ F14 = Circumference 12/ Circumference 14

F12/ F14= (V/ 2 πr12) /(V/ 2 πr14)

=r14/ r12

= m14/ m12

= 14.0u /12.0 u

= 1.17

In conclusion, the ratio of the frequency of revolution of the two types of ion is 1.17

Explanation:

Translation:

Electrons in an atom are identified by four quantum numbers. Two electrons in one atom cannot have the same set of four quantum numbers.

This first quantum number is identified by the letter n and is named Principal quantum number. It can have only positive integer values: 1, 2,3, 4, 5, 6, 7, ...

Thus, the official name of the first quantum number is Principal quantum number.

The first quantum number indicates the main energy level which is related with the size of the orbitals: the larger the principal quantum number the farther the electron cloud is from the atomic nucleus. Thus, it is also used the name energy level to refer to the first quantum number.

Notice that the principal quantum number is also the number of the period of the element in the periodic table.