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2 years ago

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One mole of magnesium (6 × 1023 atoms) has a mass of 24 grams, as shown in the periodic table on the inside front cover of the t

extbook. The density of magnesium is 1.7 grams/cm3. What is the approximate diameter of a magnesium atom (length of a bond) in a solid block of the material? Make the simplifying assumption that the atoms are arranged in a "cubic" array, as shown in the figure. Remember to convert to SI units.

1 answer:

natka813 [3]2 years ago

7 0

This question involves the concepts of density, volume, and mass.

The approximate diameter of a magnesium atom is "3.55 x 10⁻¹⁰ m".

<h3>STEP 1 (FINDING MASS OF INDIVIDUAL ATOM)</h3>

It is given that:

Mass of one mole = 24 grams

Mass of 6 x 10²³ atoms = 24 grams

Mass of 1 atom = $\frac{24\ grams}{6\ x\ 10^{23}\ atoms}$ = 4 x 10⁻²³ grams

<h3>STEP 2 (FINDING VOLUME OF A SINGLE ATOM)</h3>

$\rho = \frac{m}{V}\\\\V=\frac{m}{\rho}$

where,

$\rho$ = density = 1.7 grams/cm³
m = mass of single atom = 4 x 10⁻²³ grams
V = volume of single atom = ?

Therefore,

$V=\frac{4\ x\ 10^{-23}\ grams}{1.7\ grams/cm^3}$

V = 2.35 x 10⁻²³ cm³

<h3>STEP 3 (FINDING DIAMETER OF ATOM)</h3>

The atom is in a spherical shape. Hence, its Volume can be given as follows:

$V =\frac{\pi d^3}{6}\\\\d=\sqrt[3]{ \frac{6V}{\pi}}\\\\d=\sqrt[3]{ \frac{6(2.35\ x\ 10^{-23}\ cm^3)}{\pi}}$

d = 0.355 x 10⁻⁷ cm = 3.55 x 10⁻¹⁰ m

Learn more about density here:

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As per mass flow equality which states that the rate of flow of mass in the inlet is equal to the product of area of the tube with the velocity of the water and the density of the tube.

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3 years ago

Consider a cyclotron in which a beam of particles of positive charge q and mass m is moving along a circular path restricted by

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A) $v=\sqrt{\frac{2qV}{m}}$

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E) $r=\frac{\sqrt{2mK}}{qB}$

Explanation:

A)

When the particle is accelerated by a potential difference V, the change (decrease) in electric potential energy of the particle is given by:

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On the other hand, the change (increase) in the kinetic energy of the particle is (assuming it starts from rest):

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B)

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C)

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From eq.(1), we can rewrite the velocity of the particle as

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Substituting into(2), we can rewrite the period of revolution of the particle as:

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D)

The angular frequency of a particle in circular motion is related to the period by the formula

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The period has been found in part C:

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