Atomic Spectra

We are given a matching question where we need to match devices with their uses. Let's look at the devices and their corresponding uses:

1. A (Transistor): - A transistor is used for Amplification of signals. Hence, A - h (Amplifier).

2. B (Diode): - A diode is commonly used as a Rectifier, as it converts alternating current (AC) to direct current (DC). Hence, B - g (Rectifier).

3. C (Zener diode): - A Zener diode is used for Voltage Regulation, maintaining a stable voltage level. Hence, C - f (Voltage Regulator).

4. D (Capacitor): - A capacitor is used in Filter Circuits to smooth out voltage fluctuations and to filter signals. Hence, D - e (Filter Circuit). Thus, the correct matching is: - A - h (Transistor as an amplifier) - B - g (Diode as a rectifier) - C - f (Zener diode as a voltage regulator) - D - e (Capacitor as a filter circuit)

Using the Rydberg formula for the frequencies of lines in the hydrogen spectrum: For a jump from the third excited state (n=4) to the first excited state (n=2), the frequency is: Comparing this with the frequency for the transition from the second orbit to the first, which is based on , we find the ratio is .

We are given that the ratio of the radii of the nuclei . The radius of the nucleus is related to its mass number as . Thus, . Substituting the given ratio, we get: Cubing both sides: Thus, . Now, the number of neutrons is , where is the mass number and is the atomic number. Since is an unknown element, we can assume the atomic number is the same as that of Aluminum (which is 13) for simplicity. Therefore: Thus, the number of neutrons in the nucleus is 73.