Complete Question
The question is the first uploaded image
Answer:
The relative separation of ¹⁴N and ¹⁵N at the detector is 2.0 cm
Explanation:
In order to gain a better understand of some concepts
Mass Spectrometer:
This is an instrument or an apparatus that can be use to measure masses of isotopes,molecular fragments and molecules,enabling precise measurement of the isotopic composition.The way it does this is by ionizing them and determining their paths in an electric and a magnetic fields.
This device is consist of three parts which include:
i) ion source
ii) mass analyser
iii) ion detector
This device sort out ions by mass,because ¹⁴N and ¹⁵N have different masses it is possible use this device to separate them
Process and Calculation:
When the mass spectrometer has been set to ultra high vacuum condition(10⁻⁶ to 10⁻⁹) by pumping it. The ¹⁴N and ¹⁵N isotopes ion is inputted into the ion source as a gas,here it would be bombarded with electrons.The resulting ions(with charge q) will then be hurried up in an electric field (having a potential difference of V) and then be assimilated into a narrow beam. this beam is sent through a magnetic field (having strength H) which deflects it into a circular trajectory with a radius(R) proportional to the mass (M).This results to a physical separation of the incoming ion beam into various outgoing beams.The desired beam is steered into the ion detector .
The mass analyser deflects the ions using the following formula:
[tex] H×q×v = M×v²÷R [/tex]
re-arranging this formula and eliminating one v
[tex] R = M×v ÷ q×H[/tex]
we are given that mass of carbon = 1.99 × 10⁻²⁶
and the radius of carbon = 12.5 cm.
The separation of the isotopes at the detector
is 2(R₁₅ - R₁₄).
[tex] R = M×v ÷ q×H [/tex]
[tex]R÷M = v ÷ (q×H) [/tex]
extracting the constants;
[tex]R₁₄ ÷ M₁₄ = R₁₂ ÷ M₁₂[/tex]:
[tex]R₁₄ = R₁₂(M₁₄÷M₁₂)[/tex]
[tex]=(12.5 cm)(2.32 × 10⁻²⁶kg ÷ 1.99 × 10⁻²⁶kg)[/tex]
[tex]=14.6 cm[tex]
[tex]R₁₅ = R₁₂(M₁₅÷M₁₂)[/tex]
[tex]=(12.5 cm)(2.49 × 10⁻²⁶kg ÷ 1.99 × 10⁻²⁶kg)[/tex]
[tex]=15.6 cm[tex]
So, [tex] 2(R₁₅ - R₁₄) = (15.6 cm - 14.6 cm) = 2.0 cm [/tex]
