The planetary model of the atom pictures electrons orbiting the atomic nucleus much as planets orbit the Sun. In this model you can view hydrogen, the simplest atom, as having a single electron in a circular orbit 1.06 × 10 − 10 m in diameter. (a) If the average speed of the electron in this orbit is known to be 2.20 × 10 6 m/s, calculate the number of revolutions per second it makes about the nucleus. (b) What is the electron's average velocity?
The planetary model of the atom pictures electrons orbiting the atomic nucleus much as planets orbit the Sun. In this model you can view hydrogen, the simplest atom, as having a single electron in a circular orbit 1.06 × 10 − 10 m in diameter. (a) If the average speed of the electron in this orbit is known to be 2.20 × 10 6 m/s, calculate the number of revolutions per second it makes about the nucleus. (b) What is the electron's average velocity?
The planetary model of the atom pictures electrons orbiting the atomic nucleus much as planets orbit the Sun. In this model you can view hydrogen, the simplest atom, as having a single electron in a circular orbit
1.06
×
10
−
10
m in diameter. (a) If the average speed of the electron in this orbit is known to be
2.20
×
10
6
m/s, calculate the number of revolutions per second it makes about the nucleus. (b) What is the electron's average velocity?
The average distance between Earth and the Sun is 1.5 ✕ 1011 m.
(a)
Calculate the average speed of Earth in its orbit (assumed to be circular) in meters per second
(b)
What is this speed in miles per hour?
Please answer B
Problem 1: Suppose A = (-3.03 m)i + (4.35 m)j, B = (2.71 m)i + (-4.29 m)j + (2.99 m)k, and D = (-2.48 m)i + (-4.5
m)j.
Part (a) What is the angle, in degrees, between D and A?
Numeric : A numeric value is expected and not an expression.
Part (b) What is the angle, in degrees, between D and B?
Numeric : A numeric value is expected and not an expression.
Kepler's third law states that for any object in a gravitational orbit,
P2∝a3P2∝a3
where PP is the orbital period of the object and aa is the average distance between the object and what it is orbiting.
In our Solar System, the natural units are distances measured in astronomical units (A.U.) and orbital periods measured in years. This can be seen for the Earth-Sun system which has an orbital period P=1P=1 year and an average distance a=1a=1 AU. Using these natural units in the Solar System, the proportionality becomes an equality, so for our Solar System:
(Pyears)2=(aA.U.)3(Pyears)2=(aA.U.)3 .
Using your mathematical prowess, determine what the orbital period in years would be for an asteroid that was discovered orbiting the Sun with an average distance of 25 astronomical units.
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