Using nanofabrication techniques, it is currently possible to construct a microscopic cantilever oscillator (like a tuning fork), which we can model as a simple harmonic oscillator with a mass of m= 8 x 10-12 kg and an angular frequency of a = 2n × 900 s-¹ Suppose that this cantilever is in its lowest possible energy state. The uncertainty in the position of the cantilever's tip in this state will be roughly the same as the width of the harmonic oscillator model's wavefunction for this energy state. a. What is the latter's width? (Note: To enter a number in scientific notation such as 5.67 x 10-5, use the format 5.67E-5.) The latter's width is m. b. The size of an average atom is about 10-10 m. How many times larger is the average atom compared to the size of the cantilever tip found from part (a)? The average atom is about times larger. Note: Round the final answer to the nearest whole number.

Using nanofabrication techniques, it is currently possible to construct a microscopic cantilever oscillator (like a tuning fork), which we can model as a simple harmonic oscillator with a mass of m= 8 x 10-12 kg and an angular frequency of a = 2n × 900 s-¹ Suppose that this cantilever is in its lowest possible energy state. The uncertainty in the position of the cantilever's tip in this state will be roughly the same as the width of the harmonic oscillator model's wavefunction for this energy state. a. What is the latter's width? (Note: To enter a number in scientific notation such as 5.67 x 10-5, use the format 5.67E-5.) The latter's width is m. b. The size of an average atom is about 10-10 m. How many times larger is the average atom compared to the size of the cantilever tip found from part (a)? The average atom is about times larger. Note: Round the final answer to the nearest whole number.