This question is about the isotopes of chromium. 0.2.1 Give the meaning of the term relative atomic mass. 0.2.2 A sample of chromium containing the isotopes 54Cr, 52Cr and 53Cr has a relative atomic mass of 52.1 The sample contains 86.1% of the 52Cr isotope. Calculate the percentage abundance of each of the other two isotopes. Abundance of 54Cr ____________ % Abundance of 53Cr ____________ % 0.2.3 State, in terms of the numbers of fundamental particles, one similarity and one difference between atoms of 54Cr and 52Cr. Similarity ____________ Difference ____________ The sample of chromium is analysed in a time of flight (TOF) mass spectrometer. 0.2.4 Give two reasons why it is necessary to ionise the isotopes of chromium before they can be analysed in a TOF mass spectrometer. 1 __________ 2 __________ 0.2.5 A 52Cr ion travels along a flight tube of length 1.25 m. The ion has a constant kinetic energy (KE) of 1.102 × 10–1 J. KE = mv² / 2 Calculate the time, in s, for the 52Cr ion to travel down the flight tube to reach the detector. The Avogadro constant, L = 6.022 × 10²³ mol–1.

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This question is about the isotopes of chromium - AQA - A-Level Chemistry - Question 2 - 2020 - Paper 1

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This question is about the isotopes of chromium. 0.2.1 Give the meaning of the term relative atomic mass. 0.2.2 A sample of chromium containing the isotopes 54Cr... show full transcript

Worked Solution & Example Answer:This question is about the isotopes of chromium - AQA - A-Level Chemistry - Question 2 - 2020 - Paper 1

Step 1

Give the meaning of the term relative atomic mass.

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Answer

Relative atomic mass is defined as the average mass of an atom of an element compared to 1/12 of the mass of an atom of carbon-12. It reflects the weighted average of all isotopes of the element based on their natural abundance.

Step 2

Calculate the percentage abundance of each of the other two isotopes.

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Answer

Let the abundance of 54Cr be x% and the abundance of 53Cr be y%. Given that:

Total abundance = 100%
Abundance of 52Cr = 86.1%

We can set up the equation:

$x + 86.1 + y = 100$

Simplifying, we find: $x + y = 13.9$

Next, using the weighted average formula for atomic mass:

$52.1 = (x)(54) + (86.1)(52) + (y)(53)$

Solving these two equations gives:

Abundance of 54Cr = 3.9%
Abundance of 53Cr = 10.0%

Step 3

State, in terms of the numbers of fundamental particles, one similarity and one difference between atoms of 54Cr and 52Cr.

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Answer

Similarity: Both 54Cr and 52Cr have the same number of protons which define them as chromium atoms.

Difference: 54Cr has 2 more neutrons compared to 52Cr, resulting in a different nucleon number.

Step 4

Give two reasons why it is necessary to ionise the isotopes of chromium before they can be analysed in a TOF mass spectrometer.

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Ionization is necessary to allow the isotopes to be accelerated by an electric field.
Ionization allows the isotopes to be influenced by magnetic fields, which are essential for their separation based on mass-to-charge ratios.

Step 5

Calculate the time for the 52Cr ion to travel down the flight tube to reach the detector.

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Answer

To find time (t), we first derive v from the kinetic energy (KE) equation:

$KE = \frac{mv^2}{2}$ We rearrange to find: $v = \sqrt{\frac{2 \cdot KE}{m}}$ Given:

KE = 1.102 × 10^-1 J
Mass of 52Cr ion, m = 52 / (6.022 × 10²³) kg Using this mass, calculate v:

Calculate m: $m = \frac{52}{6.022 \times 10^{23}} \approx 8.63 \times 10^{-26} \text{ kg}$
Calculate v using the KE: $v = \sqrt{\frac{2 \cdot (1.102 \times 10^{-1})}{8.63 \times 10^{-26}}} \approx 1.23 \times 10^{13} \text{ m/s}$
Now apply the formula for time using distance (d = 1.25 m): $t = \frac{d}{v} = \frac{1.25}{1.23 \times 10^{13}} \approx 1.02 \times 10^{-14} \text{ s}$

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This question is about the isotopes of chromium - AQA - A-Level Chemistry - Question 2 - 2020 - Paper 1

Worked Solution & Example Answer:This question is about the isotopes of chromium - AQA - A-Level Chemistry - Question 2 - 2020 - Paper 1

Give the meaning of the term relative atomic mass.

Calculate the percentage abundance of each of the other two isotopes.

State, in terms of the numbers of fundamental particles, one similarity and one difference between atoms of 54Cr and 52Cr.

Give two reasons why it is necessary to ionise the isotopes of chromium before they can be analysed in a TOF mass spectrometer.

Calculate the time for the 52Cr ion to travel down the flight tube to reach the detector.

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