The motherland calling carries him back home to Kežmarok, where he opens a private practice. He nurses teeth and fractures, amputates crushed extremities, incises, sutures, punctures ascites, delivers babies. In 1886 he marries Alžbeta Schwartzova, by whom he has five children.

By the time he was a well known doctor, he had heard about great scientific news: on November 8^th, a german physicist W.C.Rontgen discovered X-rays. On May 27^th, 1896, in the conference hall of Kežmarok’s city hall, he presented a review “About X-rays”. At that time, he was already interested in buying an X-ray machine.

The first X-ray machine was provided by the company Gebbert und Schall for 827marks. This raw machine and the modest office of a countryside doctor Alexander became the germ of medical radiology in Slovakia.
He began scanning flowers and shells, then talpas and later even animal fetuses. When he was confident enough with the new diagnostic method, he decided to scan his friend’s hand. It was on January, 6^th 1898 and the scanning took five minutes.
From 1897 to 1901 he studied x-ray image formation and production. As he succeeded in scanning bones, he focused his work on chest imaging. He closely analyzed chest x-ray images of tuberculosis of the lung.

During the first period in the history of medical x-ray imaging, very little was known about biological and bio-negative effects of the new rays. Doctor Alexander was persuaded that x-rays were harmless, and wearing of a lead apron was unnecessary. He was the first who was interested in scanning child skeleton, development and formation of ossification centers of carpal bones and vertebras. Since he was strongly convinced about the innocuity of x-rays, he persuaded his pregnant wife to undergo x-ray scanning once a month in order to study embryonic development of his future son.

Nowadays it is well known that the fetus is most sensitive to ionising radiation during the first trimester of pregnancy. But Dr. Alexander did not suspect that; therefore his son became mentally disabled.
He gave many lectures about his experience in x-rays at numerous international meetings, and published them. In 1906, after many trials, he succeeded in realizing the first plastic image, and so became founder of plastic radiography. For making plastic imaging, he first used soft, then hard x-rays, exposed twice. Putting the two scans together, he obtained a third image, and finally a last positive one that created a three-dimensional effect.
Dr. Alexander was recognized internationally (Germany, England) as being a very valuable radiologist. Unfortunately, in Hungary he had to deal with many jealous people. In 1906 the German radiological society addressed a special letter to the Faculty of Medicine of Budapest for calling attention to Dr. Alexander’s specialized accomplishment and work.

On June 18^th 1907, a central radiological laboratory was founded in Budapest, probably according to that letter. Dr. Alexander was proposed for the position of chief of the laboratory, and early in December 1907 he took oath to the chancellor of the university.
The central radiological laboratory was composed of a trans-illumination room, a dark room and a workroom. The scanning was made in the dark; exposures were long (2 minutes for bones, 10 minutes for abdomen). During the whole examination, the physician was standing in front of the patient and was not protected against x-rays.

In 1909 he qualified as a lecturer of radiology at the Faculty of Medicine in Budapest, and at the same time he founded the first department of radiology.

Between 1910 and 1912 he began studying radiological examination of kidneys and urotract, and focusing on contrast medium. After a long lasting work with x-rays, Dr. Alexander found that x-rays are not only helpful in diagnostic but also in therapy. At the time he had been working in Kežmarok, he already used x-rays for cancer treatment, especially cancer of the lower lip.
On July, 22^nd 1914 the Assembly of Professors of the University of Budapest elected him full professor of roentgenology and radiology. At that time, the fingers of his hands showed the first undesired effects of x-rays: skin changes of chronic dermatitis and hyperkeratotic lesions. He also suffered from fatigue, headache, muscle ache and high temperature.

He suddenly died from cardiovascular failure on January 15th, 1916. He was buried in Kežmarok on january 17th, 1916.