In a technique used for surface analysis called auger electron spectroscopy (AES), electrons are accelerated toward a metal surface. These electrons cause the emissions of secondary electrons (called auger electrons) from the metal surface. The kinetic energy of the auger electrons depends on the composition of the surface. The presence of oxygen atoms on the surface results in auger electrons with a kinetic energy of approximately 520 eV . Required:
What is the de Broglie wavelength of one of these electrons?

the de Broglie wavelength of one of the electrons is 5.3787 × 10⁻¹¹ m

Explanation:

Given the data in the question;

we know that; ( electron volt ) 1 eV = 1.602 × 10⁻¹⁹ J

so given that Kinetic Energy KE = 520 eV

KE = 520 × 1.602 × 10⁻¹⁹ = 8.3304 × 10⁻¹⁷ J

we know that;

Kinetic Energy = 1/2 × mv²

where m is the electron mass

and mass of electron is  9.109 × 10⁻³¹ kilograms

so

8.3304 × 10⁻¹⁷ = 1/2 × 9.109 × 10⁻¹⁷× v²

v = √[(8.3304 × 10⁻¹⁷) / (1/2 × 9.109 × 10⁻³¹)]

v = 1.3524 × 10⁷ m/s

speed of the electron v = 1.3524 × 10⁷ m/s

now, de Broglie equation;

wavelength λ = h / mv

where h is Planck constant ( 6.626 × 10⁻³⁴ m² kg / s )

so we substitute

wavelength λ = 6.626 × 10⁻³⁴ / ( 9.109 × 10⁻³¹ × 1.3524 × 10⁷)

wavelength λ = 5.3787 × 10⁻¹¹ m

Therefore, the de Broglie wavelength of one of the electrons is 5.3787 × 10⁻¹¹ m

6.4 cm (max) - 25 cm (min)

it can be observed without changing the identity of the object.

it depends on what substance you're talking about as well as many other factors. in quantum mechanics, the observation of particles affects the observers ability to measure certain properties. for example: you can know the velocity of a particle, but you can't know it's position; or you can know it's position, but not it's velocity. it's like trying to find out where a grain of sand is by throwing other grains of sand at it. once you find out where it is, it's been moved. it's also like trying to find an answer to the question of whether or not a tree falling in a forest makes a sound if nobody is there to hear it. paradoxically, the only way to find out is to be there and hear it.