# SAT Math Multiple Choice Question 890: Answer and Explanation

### Test Information

Question: 890

5. Electrons follow paths, called orbits, around the nucleus of an atom. According tothe Bohr model, the energy in joules of an atom's nth orbit containing a single electron is given by the formula shown above, where Z is the atomic number of the atom and n is the orbit number. Which of the following equations gives the atomic number ofan atom given the energy of its nth orbit (assuming there is a single electron in that orbit)?

• A. • B. • C. • D. Explanation:

A

Difficulty: Hard

Category: Passport to Advanced Math / Exponents

Strategic Advice: A question like this requires patience and concentration. As with any equation, use inverse operations to solve for (isolate) the desired variable.

Getting to the Answer: To solve the equation for Z, start by multiplying both sides of the equation by the only expression that's in the denominator on the right-hand side (n2). Then, divide by everything that Z is being multiplied by (-2.18 × 10-18). To remove the negative exponent, you can move 10-18 to the numerator (but not 2.18 because it is not being raised to a negative power): You're asked for Z (not Z 2), so take the square root of both sides of the equation to find that . This is not one of the answer choices, but you can take the square root of 1018 by writing it as (109)2, which results in the equation . This means (A) is correct.

Note: You may recall that you can't take the square root of a negative number, but electron energy is given as a negative number, which means you're multiplying a negative number by another negative number under the radical, resulting in a positive quantity.