In February 2004, scientists at Purdue University used a highly sensitive techni
ID: 2059234 • Letter: I
Question
In February 2004, scientists at Purdue University used a highly sensitive technique to measure the mass of a vaccinia virus (the kind used in smallpox vaccine). The procedure involved measuring the frequency of oscillation of a tiny sliver of silicon just 30.0 nm long) with a laser, first without the virus and then after the virus had attached itself to the silicon. The difference in mass caused a change in the frequency. We can model such a process as a mass on a spring.a. Find the ratio of the frequency with the virus attached ( fs + v) to the frequency without the virus (fs) in terms of m_v and ms, where m_v is the mass of the virus and m_s is the mass of the silicon sliver. Notice that it is not necessary to know or measure the force constant of the spring.
(fs+v)/fs = ?
b. In some data, the silicon sliver has a mass of 2.12
Explanation / Answer
a)ratio of the frequency with the virus attached ( fs + v) to the frequency without the virus (fs) ( fs + v):(fs) = m_s:(m_s+m_v) b)((2.86×10^14) /(2.02×10^15))= ((2.12×10^-16)/(2.12×10^-16+m_v)) ((2.12×10^-16+m_v)/(2.12×10^-16))=((2.02×10^15)(2.86×10^14)) (2.12×10^-16+m_v)=((2.02×10^15)(2.86×10^14))(2.12×10^-16) m_v=(2.12×10^-16)((2.02×10^15)(2.86×10^14)-1)=12.85*10^-16 g c. mass of the virus in femtograms =1.285femtogram