Explanation Kinetic energy is an energy of motion. The amount of kinetic energy that all moving objects have depends on their speed and mass. The kinetic energy is calculated by the formula, K E = − 13.6 eV n 2 Here, n is the principal quantum number (energy state). Substitute the given value of n ( 4 ) in the above equation to find K E . K E = − 13.6 eV n 2 = − 13.6 4 2 = 0.85 J The conversion of energy from J to eV is done as, 1.6 × 10 − 19 J = 1 eV 1 J = 1 1.6 × 10 − 19 eV 0.85 J = 1 1.6 × 10 − 19 × 0.85 = 0.053 eV Therefore, the kinetic energy of the hydrogen atom is 0.053 eV . The other formula for calculating the kinetic energy is given as, K E = 1 2 m v 2 Here, m is the mass of the atom. v is the speed of the hydrogen atom

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ISBN: 9780134051802

Author: Walker

Publisher: PEARSON

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The Bohr model

Students often get confused between Rutherford’s model and Bohr model of an atom. They interpret the postulates of both these models to be the same, which is incorrect. Rutherford’s model differs from Bohr’s model in the following ways:

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Chapter 31, Problem 32PCE

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The minimum speed necessary to leave both hydrogen atoms in their n=4 state after the head-on collision.

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Chapter 31, Problem 31PCE

Chapter 31, Problem 33PCE

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Consider a head-on collision between two hydrogen atoms, both initially in their ground state and moving with the same speed. Find the minimum speed necessary to leave both atoms in their n = 4 state after the collision

Consider a head-on collision between two hydrogen atoms,both initially in their ground state and moving with the sameaspeed. Find the minimum speed necessary to leave both atoms intheir n = 4 state after the collision.

(a) How much energy is required to cause an electron in hydrogen to move from the n = 2 state to the n = 5 state? in J(b) Suppose the atom gains this energy through collisions among hydrogen atoms at a high temperature. At what temperature would the average atomic kinetic energy 3/2 * kBT be great enough to excite the electron? Here kB is Boltzmann's constant. in K

Chapter 31 Solutions

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The minimum speed necessary to leave both hydrogen atoms in their n = 4 state after the head-on collision.

Solution Summary: The author explains that kinetic energy is an energy of motion.

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The minimum speed necessary to leave both hydrogen atoms in their n=4 state after the head-on collision.

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